RICHMOND — The state Senate on Thursday passed sweeping legislation meant to overhaul policing, a cause that came to the forefront here and across the country after the death of George Floyd in Minneapolis police custody in May.

The measure included provisions meant to make it easier to sue police for misconduct, but later Thursday a Senate committee killed a House bill that would have more broadly swept aside the qualified immunity that shields officers from lawsuits.

On a party-line vote in the full Senate, Democrats approved an omnibus bill that, among other things, would ban chokeholds and no-knock warrants in most situations. Sexual relations between law enforcement and people in their custody — something already prohibited in many states — would be outlawed.

The legislation also would make it easier to decertify police officers involved in wrongdoing and would establish minimum training standards for law enforcement agencies across the state. The bill now heads to the House of Delegates, which has passed criminal justice legislation of its own that is coming to the Senate.

“We have heard . . . from some who oppose this legislation that we should not allow what happened over 1,200 miles from here to dictate policy in Virginia, but we have blinders on if we think that Virginia is immune to [police] misconduct,” Sen. Mamie E. Locke (D-Hampton), who sponsored the bill, said on the floor ahead of the vote.

Some Senate Republicans said they agreed with certain aspects of the legislation but not others. They said they wished it had been presented as a series of bills rather than in a single omnibus measure — an approach more common in highly partisan Washington than Richmond.

“I think we do a lot of things better than in Washington. We actually work together a lot more. We have stand-alone bills, with more opportunities to work together,” said Sen. David R. Suetterlein (R-Roanoke). “I find myself again today with a bill that [has] many things I’d like to support, but they’ve all been wrapped up together. I fear every year we get closer to embracing this omnibus approach.”

The House and the Senate are meeting in a special session that Gov. Ralph Northam (D) called in part to address concerns over inequities in policing raised by Floyd’s killing. Legislators are also revamping the state budget, which has been hit hard by the coronavirus pandemic.

Locke’s bill is meant to chip away at qualified immunity, which shields officers from civil liability if there is any ambiguity surrounding whether their actions were justified. It would aim to do that by spelling out in the state code when officers may use force, thereby eliminating uncertainty about whether it was justified.

Under the bill, officers could not use chokeholds or fire at a moving vehicle unless someone’s life is at risk. They could not use deadly force unless they have exhausted all other means of controlling a situation.

“If there is any ambiguity of what the law is, qualified immunity kicks in,” Sen. Scott A. Surovell (D-Fairfax) said in a written statement. “By making these changes to the Code of Virginia, by clarifying what is legal and what is not legal, we are taking qualified immunity out of the mix.”

Sen. Mark D. Obenshain (R-Rockingham) and other Republicans expressed concern that officers, who at times must make split-second decisions, could “face financial ruin” for actions such as shooting someone who appeared to pose a threat but in reality did not.

“We’ve got to give them the ability to exercise some judgment or make a mistake,” Obenshain said, who noted that 13 percent of state police slots are currently vacant and another 13 percent of the force will be eligible for retirement next year. “Otherwise there’s no way we’re ever going to be able to fill these positions and keep our communities safe.”

After the Senate passed Locke’s bill, its Judiciary Committee met to consider legislation from Del. Jeffrey M. Bourne (D-Richmond) that sought to more directly eliminate qualified immunity.

“For too long we have chipped away at things or slow-walked things, and that’s why you’re seeing this uprising of activism,” Bourne said in an interview after the panel voted 12 to 3 against the bill. “The time for incrementalism on these issues is long past.”

But Republicans and some Democrats expressed concern that Bourne’s bill was too broad and promised to study the matter and take it up in the regular legislative session that begins in January.

Sen. L. Louise Lucas (D-Portsmouth) was among those who did not want to wait.

“I’m not the least bit convinced there won’t be any number of Brown and Black people who will be killed by police officers before we come back for the next session,” she said.