It was the first time any of the Democrats’ gun bills were taken up by a House committee. The Senate has passed four gun-control bills that will make their way to the same House committee later in the session.

Del. Patrick A. Hope (D-Arlington), the committee chairman, said the assault-weapons ban is still being worked on. “We hope to bring it up in short order,” he said.

The proposed ban is a top rallying cry for gun rights advocates, some of whom carried military-style weapons strapped across their chests during a huge rally Monday against gun control.

The bills that passed Friday include “universal” background checks for gun buyers, except for purchases between family members, at legal firearms shows or as part of a buyback or giveback program, or for temporary transfers that occur while the original owner is there, such as when a hunter lends a weapon to a hunting partner, as long as they remain together.

The one-handgun-per-month rule was in effect in Virginia until 2012. When it was removed, authorities reported a spike in the number of guns bought in Virginia being used for crimes in other states. Brian Moran, state secretary of public safety and homeland security, called that “a distinction we do not want.”

Also headed to the House floor is a “red flag” bill that would allow a judge, after a police investigation, to remove guns from individuals determined to be at risk to themselves or others. Gun rights supporters who flooded Richmond on Monday had protested that the measure would allow a vengeful neighbor or spouse to report someone without cause, but Del. Richard C. “Rip” Sullivan Jr. (D-Fairfax), sponsor of the bill, said the law “will not be used as a cudgel by an angry neighbor or angry brother-in-law. There are stiff penalties for false reports.”

Democrats, who wrested control of the majority from Republicans in November partly on the promise of enacting stiffer gun laws, also pushed through a measure that would allow cities, towns and counties to adopt their own gun laws, as long as none of them conflict with overarching state law.

The statute would not necessarily apply to “Second Amendment sanctuary” proclamations that have been approved in dozens of cities and towns across the state, with local officials pledging not to enforce laws they see as unconstitutional.

Other bills approved by the committee include ones that would raise the penalty from a misdemeanor to a felony for those who recklessly leave a loaded gun in a place that endangers the life of anyone under the age of 18 and would require gun owners to report a lost or stolen gun within 24 hours of becoming aware of the loss, under threat of a $250 penalty.

Committee hearings on the gun legislation have been jammed with proponents and opponents of the bills, some of whom testified emotionally.

William Shaw, a gun owner from Louisa County, called the bill allowing local gun laws “the most impractical of all of them.”

“This bill will guarantee the most number of accidents,” he said. “It’s hideously impractical.”

Proponents of universal background checks included representatives from the state attorney general’s office, the Brady Campaign to Prevent Gun Violence, the Giffords gun-control group, the Virginia Catholic Conference, the League of Women Voters, the Virginia Nurses Association, the Virginia Association of Chiefs of Police and Moms Demand Action.

Philip Van Cleave, president of the pro-gun Virginia Citizens Defense League, warned that “if we do universal background checks, the next step is universal gun registration.”

The bills often, but not always, passed on party-line votes.

One bill that drew support from Republicans says any gun owner who is the subject of a permanent protective order may not possess weapons while the order is in effect.

“Would this remove the person from the right to protect themselves in their own home?” asked Del. Thomas C. Wright Jr. (R-Lunenburg).

Del. Michael P. Mullin (D-Newport News) offered an answer. “They should think about that before they start beating their spouse,” he said. “They were subject to a permanent protective because they were violent against someone in their family. They should not have a gun.”