Rep. Luis Gutiérrez (D-Ill.) said on Sunday that President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE wants to end legal immigration to the U.S. amid the ongoing government shutdown.

"They want to end legal immigration to the United States. They say, 'Let's build a wall to keep us safe.' They say, 'Let's build a wall so that our workers don't have to compete with illegals that come across the —' but then they end legal immigration. They say, 'the lottery system, let's end it.' That's legal immigration to the United States," Gutiérrez told ABC's George Stephanopoulos on "This Week."

The congressman, who is one of the most vocal immigration advocates on Capitol Hill, made similar comments on Friday at an event outside of the Capitol.

Gutiérrez on Saturday also said he was ready to give Trump his wall along the U.S.-Mexico border if Republicans will agree to a legislative fix to preserve the Deferred Action for Childhood Arrivals (DACA) program. Trump last year announced that he was ending the Obama-era program, which protects certain immigrants brought to the U.S. illegally as children, but gave Congress time to come up with a legislative fix for them.

Rep. Mark Meadows Mark Randall MeadowsTrump reacts to Ginsburg's death: 'An amazing woman who led an amazing life' Trump carries on with rally, unaware of Ginsburg's death United Airlines, unions call for six-month extension of government aid MORE (R- N.C.), the chairman of the conservative House Freedom Caucus, fired back at Gutiérrez on Sunday, citing the ongoing government shutdown.

"We're in the middle of a shutdown, but what we're talking about is immigration. Is this an amnesty shutdown?"

Meadows went on to say a deal could be made on DACA, but the government must be funded first.

"There's a deal that can be made, but we have to open the government first," Meadows told ABC.

"We need to go back to the negotiations. We can do that if the Democrats, the Senate Democrats, here in the next 24 hours will vote to open the government back up, the negotiations will start again."

Senate Democrats and Republicans failed to reach a deadline late Friday to keep the government funded.

Democrats have blamed the shutdown on Republicans for not including a measure to fix DACA in the spending bill, while Republicans have said Democrats are holding the government hostage.