"Because of (ICE's) reputation, no one wants to talk to them because they are afraid they are going to be deported", he said.
"We should protect families that need our help and that's not what ICE is doing today", she said.
Progressive immigration rights activists - during both Republican and Democratic administrations - have come to view ICE as a rogue agency that terrorized immigrant communities.
Activists and progressive leaders are pressing on, becoming more aggressive in their push to abolish the agency, an effort many in the movement view as both a way to open up the debate over decades of bipartisan USA immigration policy and, crucially, win elections.
"The Democrats are making a strong push to abolish ICE, one of the smartest, toughest and most spirited law enforcement groups of men and women that I have ever seen", Trump tweeted from his private golf club in Bedminster, New Jersey. Kirsten Gillibrand and New York City Mayor Bill de Blasio joining the movement.
But Hemanth Gundavaram, co-director of the Immigrant Justice Clinic at Northeastern University in Boston, said ICE has been diverted from its stated mission, used as a tool by President Donald Trump to implement his "racist and xenophobic" immigration policy.
Speaking on "The Brian Lehrer Show" Friday morning, the mayor said he supported the position put forth by Alexandria Ocasio-Cortez-the 28-year-old Democratic socialist who earlier this week stunned longtime congressman Joe Crowley in a primary victory.
"Instead of being insulted with politically-motivated attacks, the men and women of ICE should be praised for risking life and limb every day in the name of national security and public safety", Johnson said.
Starting in early May, President Donald Trump ordered the arrest of adults crossing the border illegally, including those seeking asylum.
She likened the situation to what followed the white supremacist rallies last summer in Charlottesville, Virginia.
He wrote in another tweet: "To the great and courageous men and women of ICE, do not worry or lose your spirit". According to Trump, the abolition of ICE "will never happen". "I love that issue if they're going to actually do that".
"I hope they keep thinking about it because they're going to get beaten so badly", he said.
ICE has been in the center of the storm over family separations at the border.
Minority Leader Nancy Pelosi, D-Calif., "believes that ICE has been on the wrong end of far too many inhumane and unconstitutional practices to be allowed to continue without an immediate and fundamental overhaul", said her spokesman, Drew Hammill.
Alarmed by the rhetoric, the Congressional Hispanic Caucus, which has been critical of Trump's immigration agenda, developed talking points to emphasise the "inhumane and harsh" treatment of immigrants by ICE.
The activists pushing for ICE abolition, meanwhile, said they aren't anxious about potential blowback or any difficulties for Democrats facing more conservative voters, including those potentially swayed by Trump's repeated charges that Democrats favor "open borders".
In this turbulent political context, one of the first voices to call for the abolition of ICE was that of NY gubernatorial candidate Cynthia Nixon, who as an actress played the part of Miranda in the popular TV series "Sex and the City".