Updated

Many top Democrats seemingly are reluctant to speak out on the sudden momentum behind the movement to “defund the police,” as Minneapolis lawmakers announce they have the votes to do just that in their city -- the epicenter of the nation's unrest over the past two weeks following the death of George Floyd.

House and Senate Democrats on Monday held a news conference to unveil sweeping new legislation that, if passed, would increase accountability of police officers by banning certain practices and curbing immunity from legal consequences stemming from acts committed in the line of duty.

During the news conference, though, the “defund the police” calls were not explicitly discussed as lawmakers guided the discussion more toward reform efforts.

'DEFUND THE POLICE' WRESTS SUPPORT FROM POLITICIANS COAST-TO-COAST

Later, House Speaker Nancy Pelosi, D-Calif., and Senate Minority Leader Chuck Schumer, D-N.Y., were asked by a CNN reporter if they supported the movement to defund the police entirely.

“That’s a local decision,” Pelosi said, noting that they would have “those debates at the local level.”

“That doesn’t mean we’re going to pile more money on to further militarize police,” she reportedly added, without directly addressing whether she supports the radical step some local activists are demanding.

Sen. Kamala Harris, D-Calif., was in a similar position on ABC’s “The View,” where she avoided directly answering whether she backs the movement.

“We need to reimagine how we are achieving public safety in America,” she said, noting that cities that direct “one-third of the budget to police” instead of “public schools, job training and job creation—come on. We have to be honest with this.”

Fox News is told top House Democrats warned rank-and-file members on a conference call Monday about being sucked into a debate about defunding the police, amid concerns about its impact on their election chances.

Washington, D.C., Mayor Muriel Bowser last week dedicated "Black Lives Matter Plaza" on a street near the White House. Later, protesters added an equals sign and the words "defund the police" to the mural. When asked whether she would remove the unauthorized changes to her government's street mural on ABC's "This Week," Bowser was noncommittal.

"We certainly are very proud of the D.C. mural that we commissioned and our department of public works and local artists installed. It is an affirmative piece of art," she said, not answering the host's question. When asked again, Bowser said, "[i]t's not a part of the mural and we certainly encourage expression, but we are using the city streets for city art... I actually haven't had an opportunity to review it."

When asked where House Majority Whip Jim Clyburn, D-S.C., stood on the issue, his office told Fox News that: "Whip Clyburn supports restructuring police departments to ensure resources are deployed to protect and serve all Americans equitably."

MINNEAPOLIS MAYOR JACOB FREY REJECTS CITY COUNCIL'S PUSH TO DEFUND POLICE, DESPITE VETO-PROOF MAJORITY

Some Democrats, though, have started to speak out against these demands.

Presumptive Democratic presidential nominee Joe Biden initially was mum on the issue, but on Monday afternoon, his campaign released a statement saying Biden “does not believe that police should be defunded.”

Biden, though, was slammed by the Trump campaign Monday morning, prior to the campaign releasing the statement, as “weak” and “unable to stand up to the most extreme elements in his party.”

Sen. Cory Booker, D-N.J., over the weekend also said that he did not support the movement and said that while he understands “the sentiment and the substance behind the slogan” of “defund the police,” he said, “it’s not a slogan I’ll use.”

And last week, Rep. Karen Bass, the leader of the influential Congressional Black Caucus, came out against slashing police budgets.

BIDEN COMES OUT AGAINST 'DEFUND THE POLICE'

"No, I don't believe that we should defund police departments," Bass said Wednesday.

The comments come amid calls to “defund the police” in places like Minneapolis, where George Floyd died in police custody, New York City and beyond.

Minneapolis’ left-leaning City Council members on Sunday announced a veto-proof push to disband the Minneapolis police, even as the mayor made clear he does not support abolishing the department.

What defunding the police looks like is different in various localities. In Minneapolis, the supermajority of the City Council seemingly supports a complete structural dismantling of the department. In other places, departments would remain in place but get fewer government resources, with some of their funding directed toward social justice programs.

Meanwhile, Los Angeles Mayor Eric Garcetti plans to make cuts up to $150 million to the city’s police department and redistribute the money to “black communities and communities of color.”

CLICK HERE TO GET THE FOX NEWS APP

New York City Mayor Bill de Blasio announced over the weekend that he will be diverting funding for the New York Police Department toward social services.

“The details will be worked out in the budget process in the weeks ahead. But, I want people to understand that we are committed to shifting resources to ensure that the focus is on our young people,” de Blasio said.

Fox News' Tyler Olson and Chad Pergram contributed to this report.