House Republicans wrapped up impeachment hearings against Alejandro N. Mayorkas, the homeland security secretary, on Thursday, a little more than a week after the proceedings began, racing to charge him with failing to enforce the nation’s immigration laws.

The Republicans are moving ahead without evidence that Mr. Mayorkas has committed high crimes or misdemeanors, the constitutional standard for impeachment, effectively seeking to remove him for immigration policies they argue have imperiled the American public.

They plan to bring charges against Mr. Mayorkas as early as the end of this month, without having featured testimony from him or any other witness from the Biden administration to publicly answer for his conduct, or a single constitutional expert to support their argument that he is guilty of impeachable offenses.

Republicans on the House Homeland Security Committee invited the secretary to testify at Thursday’s hearing, but when Mr. Mayorkas asked for a different date, they told him instead to submit a written statement by Jan. 28.

“The truth is that Secretary Mayorkas has disregarded court orders, laws passed by Congress and has lied to the American people,” Representative Mark E. Green, Republican of Tennessee and the chairman of the panel, said during the hearing. “Who wants a secretary that can just disregard the fundamental pillars of the Constitution? We cannot tolerate that, whether they are a Republican or Democrat.”

The Republican push to impeach Mr. Mayorkas comes as right-wing lawmakers attack the Biden administration’s immigration policies and threaten to vote against funding the government unless officials crack down on migration at the U.S. border with Mexico. G.O.P. leaders have insisted Mr. Mayorkas is personally responsible for failing to end a surge of illegal migration and drug trafficking at the border that even Democrats acknowledge has worsened in recent years.

The committee invited two grieving mothers — one who lost a daughter to fentanyl poisoning, and another whose daughter was murdered by a member of the Salvadoran gang MS-13 who had been paroled into the United States — to deliver the final in-person arguments against Mr. Mayorkas on Thursday. Both tearfully testified that they held the secretary responsible for the deaths of their children.

But the lack of direct evidence against the secretary has angered Democrats, who accused Republicans of attempting to rush his impeachment through the House in order to please hard-liners in their base.

“This isn’t a real impeachment — it’s a predetermined, preplanned, partisan political stunt,” said Representative Bennie Thompson of Mississippi, the senior Democrat on the panel. “You cannot impeach a cabinet secretary because you don’t like a president’s policies,” he added.

Republicans have defended their process as complete, pointing to the findings of a monthslong investigation they conducted before the hearings that included testimony from more than two dozen witnesses, including senior Border Patrol agents. After Thursday’s hearing, all 18 Republican members of the panel signaled they were ready to move ahead with impeachment.

“It is unmistakably clear to all of us — and to the American people — that Congress must exercise its constitutional duty and impeach Secretary Mayorkas,” they wrote in a joint statement.

House Republicans have been threatening to impeach Mr. Mayorkas for the past year, and in that time, hauled him in before the panel twice to excoriate him over his department’s policies. They have also accused him of lying to lawmakers when he said the administration had “operational control” of the border, though Mr. Mayorkas explained that the Border Patrol defines the term differently than statute does.

The case against Mr. Mayorkas stalled for several months last year, as Republican leaders found themselves short of the votes to impeach him, with some of their members skeptical about using a grave constitutional remedy to settle what is essentially a policy dispute. But the hard right has pressed for the move, and G.O.P. leaders now believe they have enough support for charges to squeak through the House.

The panel is proceeding at a breakneck pace, skipping efforts to subpoena any firsthand witnesses to testify to Mr. Mayorkas’s actions or support their assertion that he has intentionally endangered the country.

Democrats have cried foul at the process, and on Thursday invited a professor who noted that impeaching Mr. Mayorkas would not fix the problems Republicans accuse him of creating.

“Impeachment will have no impact on resources available to the border,” said Deborah Pearlstein, a law professor at Princeton University, “and it will have no impact on the policies pursued by this administration at all.”

The push to impeach Mr. Mayorkas has coincided with his participation in a high-stakes set of bipartisan talks in the Senate to reach a border enforcement compromise that would set new policies on asylum and detention. Senate Republicans and Democrats have signaled they are close to finalizing such a deal, which Republicans have demanded as the price for sending more emergency military assistance to Ukraine for its war against Russia.

But the hard right has rebelled against the emerging deal, and Speaker Mike Johnson has said he is reluctant to put it to a vote unless it closely reflects a severe border enforcement measure the House passed last year with no Democratic support.

“Congress has failed to fix the broken immigration system for decades, and they currently have an opportunity to do so,” Mia Ehrenberg, a spokeswoman for the Department of Homeland Security, said in a statement. “Instead of wasting time on a baseless impeachment effort, the House majority should join Senate Republicans and Democrats working with Secretary Mayorkas to fix our broken immigration laws and properly fund the department.”

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