Alejandro N. Mayorkas, the homeland security secretary, said on Sunday that he was not dwelling on congressional Republicans’ continued efforts to impeach him over his handling of the southern border.

“They’re baseless allegations, Kristen, and that’s why I really am not distracted by them and focused on the work of the Department of Homeland Security,” he said in an interview on NBC’s “Meet the Press” with Kristen Welker. “I’ve got a busy day today. After the show, a busy day of work. I’ve got a busy day Monday, Tuesday, Wednesday and so on.”

Republican leaders in the House suffered a stunning defeat last week in their first effort to impeach Mr. Mayorkas, but they have vowed to try again.

They have contended that Mr. Mayorkas should be charged with high crimes and misdemeanors for not enforcing immigration laws. Mr. Mayorkas has denied these claims and said that the United States allows for a presidential administration to have flexibility on border policies.

He said that it was up to Congress to fix a “broken” immigration system, just days after a bipartisan deal to overhaul policies at the southern border was stymied in the Senate.

“It certainly is a crisis and, well, we don’t bear responsibility for a broken system,” Mr. Mayorkas said. “And we’re doing a tremendous amount within that broken system. But fundamentally, fundamentally, Congress is the only one who can fix it.”

Mr. Mayorkas, the first Latino to run the department, has testified before Congress more than any other member of President Biden’s cabinet — a total of more than two dozen times. He has told House Republican officials that their effort to impeach him will not affect the work he is doing and has maintained that he will not resign if their push is successful.

In a January letter to Representative Mark E. Green, Republican of Tennessee and the chairman of the Homeland Security Committee, Mr. Mayorkas said the drive to impeach him had not shaken him.

“I assure you that your false accusations do not rattle me and do not divert me from the law enforcement and broader public service mission to which I have devoted most of my career and to which I remain devoted,” he wrote.

One of the Republicans who broke with his party to vote against the impeachment effort, Representative Mike Gallagher Wisconsin, said on Saturday that he would not seek re-election.

Mr. Gallagher wrote in a Wall Street Journal opinion piece last week that the impeachment effort was misguided.

“I disagree with my Republican colleagues who voted on Tuesday to impeach Mr. Mayorkas,” he wrote. “Impeachment would not only fail to resolve Mr. Biden’s border crisis but also set a dangerous new precedent that will be used against future Republican administrations.”