WASHINGTON—Dining at his oceanside resort in Florida on Friday, President Donald Trump was surprised to learn that national security adviser Mike Flynn was sitting at a nearby table, a person familiar with the event said.
“What is he doing here?” the president said, describing the man who was once at the center of his political orbit as “very controversial.”
The moment epitomizes how quickly fortunes can change amid the chaos that has defined the opening act of Mr. Trump’s presidency. In just a few weeks, the nascent administration is being weighed down from within, sidetracked by dishonesty and potential ethical lapses as well as attacks from his own supporters and fellow Republicans.
Mr. Flynn on Monday became the first casualty of that chaos, resigning as head of the National Security Council after he lost the president’s trust by failing to fully disclose his conversations with Russian officials to senior White House officials, including Vice President Mike Pence.
“It’s a dysfunctional White House, and nobody knows who’s in charge,” Sen. John McCain (R., Ariz.) told reporters on Tuesday.
Several congressional committees are investigating the possible role that Russia played in the 2016 elections. In addition, the Republican-run House Oversight Committee has begun examining issues related to conflicts of interest and protection of classified information in the new White House.
The administration’s senior ranks are creating headlines of their own as they jockey for power and influence with the president.
Kellyanne Conway, a senior adviser, faces calls for an ethics investigation and possible disciplinary action. The Office of Government Ethics wrote to the White House on Tuesday that there was “strong reason” to believe Ms. Conway violated ethics rules for endorsing the product line of Mr. Trump’s daughter during a television interview.
Ms. Conway also appeared to be out of the loop, going on television Monday to declare that the president had “full confidence” in Mr. Flynn only to be contradicted within the hour by press secretary Sean Spicer, who said the president was still evaluating the national security adviser’s status.
Chief of Staff Reince Priebus also found himself with unwanted attention when Newsmax Chief Executive Christopher Ruddy, one of the president’s friends and a member of the Mar-a-lago oceanside resort, on Sunday talk shows expressed frustration with Mr. Priebus’s performance. Messrs. Priebus and Jared Kushner, the president’s son-in-law and top adviser, later called Mr. Ruddy and briefed him on plans to improve communications going forward. The media executive now has reversed his opinion of the White House team.
Still, Mr. Priebus has other detractors.
“Reince Priebus walked Mike Flynn to the gallows,” Roger Stone, a former political adviser for Mr. Trump, said on Tuesday, calling it a “Pearl Harbor moment” for Trump supporters. “Trump loyalists are fed up with Reince Priebus and Sean Spicer whose loyalties are to the Republican National Committee, and not to the president.”
Two days before Mr. Trump’s inauguration, Mr. Kushner and senior adviser Steve Bannon took a red-eye flight from New York to Washington to ease concerns about Mr. Flynn from incoming cabinet members, including eventual Secretary of State Rex Tillerson and Defense Secretary Jim Mattis.
The administration later installed Keith Kellogg as Mr. Flynn’s staff chief and elevated the role of homeland security adviser, Tom Bossert, to give him equal sway inside the White House as Mr. Flynn.
On Tuesday, Mr. Kellogg, who was named interim national security adviser following Mr. Flynn’s resignation, led an all-hands meeting of National Security Council staff. The message was direct and simple, said one attendee: Keep working hard, and please, don’t quit.
Mr. Flynn’s resignation surprised Japanese officials, who said the adviser was key in orchestrating the Trump administration’s fledgling relationship with Tokyo. Mr. Flynn had attended “nearly all of the events” during Prime Minister Shinzo Abe’s visit to Washington and Florida last week, officials said.
He sat in on the meeting between Messrs. Trump and Abe at the White House on Friday, and, at Mar-a-Lago, was involved in drafting statements to condemn North Korea’s launching of a ballistic missile into the Sea of Japan over the weekend.
Mr. Flynn loomed large in the country’s bilateral interactions with Japan, due in part to the fact that Mr. Tillerson hadn’t yet been confirmed, officials said. Mr. Flynn visited Tokyo and was the only attendee at Mr. Trump’s November meeting with Mr. Abe at Trump Tower, after an initial greeting session with a bigger group.
“We tried to help him succeed,” one senior administration official said. “It was absolute dysfunction.”
The intrigue is likely to continue.
Senior White House advisers have suggested to cabinet secretaries or nominees that they need to be consulted on all personnel and policy decisions, creating friction between the agencies and the White House officials who have been permanently stationed inside their buildings.
Many of the U.S. ambassadorships remain unfilled, a result of a standoff between Mr. Tillerson and Mr. Priebus, the chief of staff, said people familiar with the process.
Mr. Trump had told Mr. Tillerson he would have a say in appointing some key ambassadorships, including Canada and Switzerland, those people said. Mr. Priebus subsequently got the president to approve names for those positions—including several top donors to the RNC—without consulting the secretary of state, which angered Mr. Tillerson.
Spokesmen for the State Department and Mr. Priebus didn’t respond to requests for comment.
The infighting has sown growing insecurity among Mr. Priebus and his top aides.
When Mr. Trump called Mr. Bossert, the homeland security adviser, into his office earlier this month, deputy chief of staff Katie Walsh spotted him entering the Oval Office and sprinted down the hallway to alert her boss, Mr. Priebus, according to a person familiar with the events. Mr. Priebus subsequently dashed into the office, where he reprimanded Mr. Bossert—in front of Mr. Trump—for trying to meet with the president without him.
“Reince is doing a great job,” Mr. Trump told reporters at the White House on Monday. “Not a good job. A great job.”
Mr. Trump avoided questions about Mr. Flynn Monday during a news conference with Canadian Prime Minister Justin Trudeau. Consequently, reporters lined up and spent three hours waiting outside Mr. Spicer’s office to get an update.
When Mr. Trump walked by on his way to the Oval Office, they shouted questions about him about his national security adviser.
Mr. Trump ignored them, and turned to a picture on the wall of the audience that witnessed his inaugural speech on Jan. 20. Mr. Trump ignited the first controversy of his presidency by ordering Mr. Spicer to push back on widely reported data that showed that the crowd witnessing his inauguration was smaller than his predecessor’s audience.
“Where did all these people come from? Ohhh,” Mr. Trump said, feigning surprise as he leaned over the picture and pointed to individual people in the crowd.
—Peter Nicholas, Damian Paletta, Yuka Hayashi, Shane Harris and Richard Rubin contributed to this article.