Minnesota Sen. Amy Klobuchar on Sunday bucked calls by fellow high-profile Democrats to abolish the U.S. Immigration and Customs Enforcement (ICE) agency, putting a damper on the far-left proposal that has gained mainstream traction in recent days.

"We are always going to need immigration enforcement," Klobuchar said on ABC's "This Week."

"I think we know that," she added. "We are a major country with major borders, so to me, the issue is what are those policies."

New York Sen. Kirsten Gillibrand, a potential 2020 presidential candidate, and Mayor Bill de Blasio both advocated abolishing ICE this week. Another possible presidential candidate, California Sen. Kamala Harris, has said that officials should "re-examine" ICE and "think about starting from scratch."

And Massachusetts Sen. Elizabeth Warren called for "replacing ICE" in a rally on Saturday.

WATCH: TRUMP SAYS DEMS WILL GET BEATEN 'BADLY' IF THEY CAMPAIGN ON ABOLISHING ICE

But Klobuchar refused to endorse that approach, and instead insisted that the focus should be on immigration policy.

"I think what has to change are the policies, and the people that are making these policies are making horrendous decisions like separating kids from their parents," she said on "This Week."

"I am just appalled by how this administration has been talking about immigrants," she added.

Also on Sunday, Connecticut Democratic Sen. Richard Blumenthal echoed Klobuchar's messaging, saying, "Abolishing ICE will accomplish nothing unless we change the Trump policies."

"We are always going to need immigration enforcement." — Democratic Sen. Amy Klobuchar

Illinois Democratic Sen. Tammy Duckworth weighed in on CNN's "State of the Union," saying: "You abolish ICE now, you still have the same president with the same failed policies."

The growing influence behind the push to get rid of ICE was underscored earlier this week with liberal primary challenger Alexandria Ocasio-Cortez's shocking victory over Rep. Joseph Crowley, D-N.Y., a member of party leadership.

Ocasio-Cortez emphasized her support for abolishing ICE during the campaign, and even protested outside an ICE center in Texas.

Speaking exclusively to Fox News' Maria Bartiromo on "Sunday Morning Futures," President Trump said Democrats who campaign on abolishing ICE risk catastrophe at the ballot box.

"Well, I hope they keep thinking about it," Trump said. "Because they’re going to get beaten so badly.

"You know ICE, these are the guys that go in and take MS-13, and they take them out," Trump added. "Because they're much tougher than MS-13, like by a factor of 10. ... You get rid of ICE, you’re going to have a country that you’re going to be afraid to walk out of your house."

Fox News' Alex Pappas contributed to this report.