Mr. Hegseth’s wife, Jennifer, a former Fox News producer, is not a Defense Department employee, but she has traveled with him overseas and drawn criticism for accompanying her husband to sensitive meetings with foreign leaders.

Mr. Hegseth’s brother Phil and Tim Parlatore, who continues to serve as his personal lawyer, both have jobs in the Pentagon, but it is not clear why either would need to know about upcoming military strikes aimed at the Houthis in Yemen.

The previously unreported existence of a second Signal chat in which Mr. Hegseth shared highly sensitive military information is the latest in a series of developments that have put his management and judgment under scrutiny.

Unlike the chat in which The Atlantic was mistakenly included, the newly revealed one was created by Mr. Hegseth. It included his wife and about a dozen other people from his personal and professional inner circle in January, before his confirmation as defense secretary, and was named “Defense | Team Huddle,” the people familiar with the chat said. He used his private phone, rather than his government one, to access the Signal chat.

The continued inclusion following Mr. Hegseth’s confirmation of his wife, brother and personal lawyer, none of whom had any apparent reason to be briefed on operational details of a military operation as it was getting underway, is sure to raise further questions about his adherence to security protocols.

The chat revealed by The Atlantic in March was created by President Trump’s national security adviser, Mike Waltz, so that the most senior national security officials across the executive branch, such as the vice president, the director of national intelligence and Mr. Hegseth, could coordinate among themselves and their deputies ahead of the U.S. attacks.

Mr. Waltz took responsibility for inadvertently adding Jeffrey Goldberg, the editor of The Atlantic, to the chat. He called it “Houthi PC small group” to reflect the presence of members of the administration’s “principals committee,” who come together to discuss the most sensitive and important national security issues.

Mr. Hegseth created the separate Signal group initially as a forum for discussing routine administrative or scheduling information, two of the people familiar with the chat said. The people said Mr. Hegseth typically did not use the chat to discuss sensitive military operations and said it did not include other cabinet-level officials.

Mr. Hegseth shared information about the Yemen strikes in the “Defense | Team Huddle” chat at roughly the same time he was putting the same details in the other Signal chat group that included senior U.S. officials and The Atlantic, the people familiar with Mr. Hegseth’s chat group said.

The Yemen strikes, designed to punish Houthi fighters for attacking international cargo ships passing through the Red Sea, were among the first big military strikes of Mr. Hegseth’s tenure.

After The Atlantic disclosed that Mr. Hegseth had used Mr. Waltz’s Signal group to communicate details of the strikes as they were being launched, the Trump administration said he had not shared “war plans” or any classified information, an assertion that was viewed with tremendous skepticism by national security experts.

In the case of Mr. Hegseth’s Signal group, a U.S. official declined to comment on whether Mr. Hegseth shared detailed targeting information but maintained that there was no national security breach.

“The truth is that there is an informal group chat that started before confirmation of his closest advisers,” the official said. “Nothing classified was ever discussed on that chat.”

Sean Parnell, the chief Pentagon spokesman, did not respond to several requests for comment before this article was published.

After it was published, Mr. Parnell responded on social media. “Another day, another old story — back from the dead,” he wrote. “There was no classified information in any Signal chat, no matter how many ways they try to write the story.”

The “Defense | Team Huddle” Signal chat until recently included about a dozen of Mr. Hegseth’s top aides, including Joe Kasper, Mr. Hegseth’s chief of staff, and Mr. Parnell.

The chat also included two senior advisers to Mr. Hegseth — Dan Caldwell and Darin Selnick — who were accused of leaking unauthorized information last week and were fired.

Mr. Caldwell and Mr. Selnick were among three former top Pentagon officials who proclaimed their innocence in a public statement on Saturday in response to the leak inquiry that led to their dismissals.

On Sunday, another former Defense Department official, John Ullyot, who left the department last week, said in an opinion essay for Politico that the Pentagon “is in disarray under Hegseth’s leadership” and suggested that Mr. Trump should remove him.

When Mr. Goldberg released details of what Mr. Hegseth put into the Signal chat created by Mr. Waltz regarding the upcoming strikes in Yemen, Mr. Trump defended him and said he had done nothing wrong.

In a statement, Anna Kelly, a White House spokeswoman, did the same after the latest revelation. “No matter how many times the legacy media tries to resurrect the same nonstory, they can’t change the fact that no classified information was shared,” Ms. Kelly said.

Some congressional Democrats said it was fresh proof that Mr. Hegseth should be removed.

“Every day he stays in his job is another day our troops’ lives are endangered by his singular stupidity,” said Senator Tammy Duckworth, Democrat of Illinois and a combat veteran.

Senator Jack Reed of Rhode Island, the senior Democrat on the Armed Services Committee, added: “If true, this incident is another troubling example of Secretary Hegseth’s reckless disregard for the laws and protocols that every other military service member is required to follow.”

While the Signal chat created by Mr. Waltz for senior officials was criticized for sharing details of a military operation on an encrypted but unclassified app, the participants — other than Mr. Goldberg of The Atlantic, who appears to have been added accidentally — were senior government officials with reason to track the progress of the attack.

But some of the participants in the group chat created by Mr. Hegseth were not officials with any apparent need to be given real-time information on details of the operation.

Jennifer Hegseth has drawn attention for the access her husband has given her. Mr. Hegseth brought her into two meetings with foreign military counterparts in February and early March where sensitive information was discussed, a development first reported by The Wall Street Journal.

Mr. Parlatore, who has been Mr. Hegseth’s personal lawyer for the last eight years, was commissioned as a Navy commander in the Judge Advocate General’s Corps about a week before the Yemen strikes were initiated.

In an interview before rejoining the military, Mr. Parlatore told The New York Times that he would work with Mr. Hegseth’s office to improve training for the military’s uniformed lawyers.

Mr. Hegseth’s brother Phil works inside the Pentagon as a liaison to the Department of Homeland Security and as a senior adviser to the defense secretary.

One person familiar with the chat said Mr. Hegseth’s aides had warned him a day or two before the Yemen strikes not to discuss such sensitive operational details in his Signal group chat, which, while encrypted, is not considered as secure as government channels typically used for discussing highly sensitive war planning and combat operations.

It was unclear how Mr. Hegseth, a veteran and former Fox News host who before his confirmation in January had never previously served in a high-level government position, responded to those warnings.

Many of those in Mr. Hegseth’s inner circle during his first months in the Pentagon were combat veterans with deep experience in the military but little firsthand knowledge of how the government operates at the highest levels.

Several of these staff members encouraged Mr. Hegseth to move the work-related matters in the “Defense | Team Huddle” chat to his government phone. But Mr. Hegseth never made the transition, according to some of the people familiar with the chat who spoke on condition of anonymity to discuss internal deliberations.

The Pentagon’s acting inspector general announced earlier this month that he would review Mr. Hegseth’s Yemen strike disclosures on the Signal chat that included top Trump aides.

“The objective of this evaluation is to determine the extent to which the secretary of defense and other DoD personnel complied with DoD policies and procedures for the use of a commercial messaging application for official business,” the acting inspector general, Steven Stebbins, said in a notification letter to Mr. Hegseth.

It’s not clear whether Mr. Stebbins’s review has uncovered the Signal chat that included Mr. Hegseth’s wife and other advisers.

Mr. Stebbins started the review in response to a joint bipartisan request from Senator Roger Wicker of Mississippi, the Republican chairman of the Armed Services Committee, and Mr. Reed.

Beyond the controversy of the Signal chat, Mr. Hegseth’s office has been shaken by the sudden firings of Mr. Caldwell, Mr. Selnick and Colin Carroll, all top advisers to the defense secretary. They were escorted from the Pentagon last week after being accused of leaking sensitive information.

The dismissals and turmoil around the inspector general’s investigation have raised tensions and prompted talk of more resignations, according to current and former defense officials.

Among those considering leaving are Mr. Kasper, Mr. Hegseth’s chief of staff, who helped lead the leak investigation that resulted in his colleagues’ dismissal but has not been implicated in wrongdoing, according to senior defense officials.

In the wake of the report in The Atlantic disclosing the first Signal chat, Mr. Hegseth and other senior administration officials repeatedly denied that any classified information was shared among the participants.

“Nobody was texting war plans, and that’s all I have to say about that,” Mr. Hegseth told reporters. At a Senate hearing, Tulsi Gabbard, the director of national intelligence, echoed Mr. Hegseth’s assertion that no classified information was shared.

But other former senior defense officials said texts describing launch times and the type of aircraft being employed before a strike would be classified information that, if leaked to the enemy, could have jeopardized pilots’ lives.