Homeland Security Secretary Alejandro Mayorkas, who narrowly escaped impeachment last week, said Sunday that the Biden administration doesn't "bear responsibility for a broken system," demanding Congress enact legislation to mitigate what has become an illegal migration crisis during this election year.

"No doubt there is gridlock in Congress. But do you bear responsibility for what is happening at the border with the president himself? It's called a crisis," NBC host Kristen Welker asked during an interview with Mayorkas on "Meet the Press."

"It certainly is a crisis. And we don't bear responsibility for a broken system. And we're doing a tremendous amount within that broken system. But fundamentally … Congress is the only one who can fix it," Mayorkas said.

"There is no question that we have a broken system," he added. "There is no question that we have a challenge, a crisis at the border. And there is no question that Congress needs to fix it. And we're doing everything we can within that broken system, short of legislation to address what is a not just a challenge for the United States but one throughout our region."

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Since Mayorkas took the helm at the Department of Homeland Security three years ago, Welker noted, the asylum case backlog has more than tripled since 2019 and more migrants have crossed the border illegally in 2023 than ever before. She pointed to how Mayorkas himself has said that more than 85% of migrants crossing the border illegally are being released into the U.S. as they await their court dates.

"Let's just put impeachment aside for a minute. Why do you deserve to keep your job, Mr. Secretary?" she asked. 

"The data that you cite is a powerful example of why we need legislation to fix what everyone agrees is a broken immigration system," Mayorkas said. "Before the last three years, that case backlog, which is about 3 million cases, has been growing year over year over year. The time between when we encounter an individual at the border and the time of final adjudication of an asylum claim case has been years, five to seven years, for years and years."

"I remember when I entered the Department of Homeland Security in 2009, we were wrestling with these very same issues. The system has not been fixed for 30 years. A bipartisan group of senators have now presented us with the tools and resources we need – bipartisan group. And yet, Congress killed it before even reading it," he said.

Mayorkas was referring to how the U.S. Senate on Wednesday failed to pass a $118 billion supplemental spending agreement that included aid for Ukraine, Israel and Taiwan, as well as an ambitious border security and immigration package that drew widespread opposition from conservative Republicans in both chambers since its release just days earlier. Wednesday's vote was 50-49. It needed 60 votes to pass. The vote went mostly along party lines, except for five Democrat no votes and four Republicans voting yes.

Welker pressed Mayorkas on why President Biden would not shut down the border immediately – as Republicans have called on him to do – and "just let the courts try to stop him."

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"We have taken executive actions already. We continuously review what options are available to us, but those are always challenged in the courts, and whether or not they see the light of day and actually are able to be operationalized is an open question," Mayorkas said. "That is why the bipartisan group of senators actually prepared and presented a piece of legislation that would … base it in statute, the ability to close the border for a limited period of time, an extreme measure, and would it would be immune from court challenge because it is statutorily based."

"If it were done legislatively, no doubt you wouldn't have these these legal challenges, but isn't trying to do something better than doing nothing at all? Why doesn't President Biden try to shut down the border? Are you encouraging him to do that?" Welker insisted.

"Well, we have already taken important steps. We certainly haven't done nothing. I will tell you, we issued a regulation that circumvention of lawful pathways that increased, that actually created a rebuttable presumption of ineligibility for asylum seekers if they did not avail themselves of the lawful pathways that we built. And so we've done a tremendous amount. It's very important to remember we have removed, returned or expelled more individuals in the past three years than the prior administration did in all four."

Asked if he was considering reinstating the Remain in Mexico policy on Sunday, Mayorkas told Welker, "First of all, it depends upon Mexico's agreement. And Mexico has articulated publicly that it will not allow the re-implementation of Remain in Mexico, number one. Number two, it's been challenged in the courts. And number three, remember something, that Remain in Mexico was implemented in January of 2019. In 2019, there was almost a 100% increase in the number of encounters at our southwest border over 2018."

The Republican-led House of Representatives on Tuesday failed to impeach Mayorkas over his handling of the crisis at the southern border. It was considered a crushing defeat for the Republican majority, which held hearings throughout 2023 on Mayorkas' apparent "dereliction of duty" and additional hearings on the impeachment articles themselves this year. 

Lawmakers accused Mayorkas of disregarding federal law with "open border policies" that have made the ongoing crisis at the southern border worse. They have pointed to the rolling back of Trump-era policies, like border wall construction and Remain in Mexico, and reducing interior enforcement and expanding "catch-and-release." They say it has fueled record numbers at the southern border, breaching the 300,000 mark in December.

Fox News' Elizabeth Elkind and Adam Shaw contributed to this report.