Activists and political leaders calling for state and federal police reform said Wednesday that former Minneapolis police officer Derek Chauvin's conviction for murdering George Floyd shouldn't slow that push.

"This white hot spotlight that has been on Minnesota can't leave now," Democratic Gov. Tim Walz said Wednesday morning in a "CBS This Morning" interview. "My fear: Everybody packs up and we think we've got this."

Chauvin's conviction on Tuesday is the first time in Minnesota history that a white police officer was convicted of murdering a Black person. While activists hailed the Hennepin County jury's decision, they point to last week's fatal police shooting in Brooklyn Center — and other cases around the country — as evidence that more laws need to be changed.

"Unfortunately the recent horrific killing of Daunte Wright in Brooklyn Center shows that more urgent action is needed to change state law," leaders of a coalition of 38 progressive groups wrote in a letter Wednesday to state leaders.

But in remarks on the floor of the state Senate on Wednesday morning, Republican Majority Leader Paul Gazelka suggested that the Chauvin verdict demonstrated that the current system worked.

"As we watched the verdict yesterday, I don't think anybody can say that justice wasn't served and so we have a process that works," Gazelka, R-East Gull Lake, said in response to a DFL colleague who pressed him on whether the Republican majority would take up measures sought by Walz and his fellow Democrats.

Gazelka said the Senate Judiciary Committee would hold hearings at the end of next week on some measures sought by the House Democratic majority. But he offered no assurances of any votes by the full Senate.

Meanwhile, state Senate Republicans are pushing a bill for harsher penalties against people arrested while protesting. Individuals could be subject to loss of student financial aid and other government benefits, among other consequences.

Early Thursday, the Minnesota House passed a public safety package on a 70-63 vote that incorporates many police accountability measures sought by activists. That includes new limits on when police can pull over vehicles.

Among the violations no longer eligible for a stop would be expired tabs and items hanging from a rearview mirror. Police say Wright was pulled over for expired plates.

"Yes, the verdict was important," said Rep. Carlos Mariani, DFL-St. Paul. "But it should just be the beginning, not the end."

Other provisions in that package would let local communities form police oversight groups and would bar police officers from affiliation with known hate groups.

A similar dynamic is in play in Washington, D.C., where the Biden White House and congressional Democrats hope to pass federal legislation called the George Floyd Justice in Policing Act. It aims to prohibit racial profiling in federal, state and local policing, beefs up conduct training standards and details a chokehold ban for federal law enforcement similar to what the Minnesota Legislature passed last year at the state level.

The federal bill offers "the best chance we have at passing immediate reform," U.S. Rep. Ilhan Omar, D-Minn., said in a statement.

The bill passed the U.S. House, but it faces an uncertain fate in the closely divided U.S. Senate, where it would need some support from Republicans unless Democrats decide to eliminate the filibuster rule that requires 60 votes for most legislation to advance.

"I sincerely hope that we are able to make some progress but it's not going to be easy," Sen. Tina Smith, D-Minn. said in a statement.

Her Democratic colleague, Sen. Amy Klobuchar, pledged in a statement of her own to "keep fighting" to pass police reform.

Sen. Cory Booker, a Democrat from New Jersey, said in a statement Wednesday he's "encouraged by the conversations I'm having with fellow senators on both sides of the aisle, and am hopeful we can find a path forward on meaningful policing reform."

Among Senate Republicans, South Carolina Sen. Tim Scott has been the leading voice on possible changes. The only Black Republican in the U.S. Senate told reporters Wednesday there were still some "outstanding issues" for him in the police reform debate, but he said he's still optimistic for a breakthrough.

"I think we are on the verge of wrapping this up in the next week or two, depending on how quickly they respond to our suggestions," Scott said.

Scott and U.S. Rep. Pete Stauber, R-Minn., championed an alternative effort last year they called the JUSTICE Act. While it doesn't go as far as what Democrats want, there are some similarities in the two proposals.

White House press secretary Jen Psaki said Wednesday that Biden feels "the bar for convicting officers is far too high; it needs to be changed."

Biden is set to give his first address to a joint session of Congress next week.

The Minnesota Legislature must adjourn its regular session by May 17, and needs to pass a two-year state budget by June 30 to avoid a government shutdown. Gazelka was noncommittal about the fate of further police accountability measures.

"There may be something, I'm not saying we will not, I just know that we have to pass the budget bills," he said.