More legislation is expected to arise over the next week or two, and some of it will have bipartisan support. Senator Kirsten E. Gillibrand, Democrat of New York, and Senator Mark Kirk, Republican of Illinois, have agreed to work together on gun trafficking legislation that would seek to crack down on illegal guns. Currently, federal law does not define gun trafficking as a crime.

Mr. Kirk is also working on a background check proposal with Senator Joe Manchin III, Democrat of West Virginia, who is considered somewhat of a bellwether among Democrats with strong gun-rights records.

Mr. Leahy’s bill would give law enforcement officials more tools to investigate so-called straw purchasing of guns, in which people buy a firearm for others who are prohibited from obtaining one on their own.

Ms. Feinstein was joined on Thursday by several other lawmakers, including Representative Carolyn McCarthy of New York, who will introduce companion legislation in the House, and Senator Richard Blumenthal of Connecticut, who emotionally recalled the day when the children and adults were gunned down in Newtown. “I will never forget the sight and the sounds of parents that day,” he said. Several gun violence victims, relatives of those killed and others gave brief statements of support for the bill.

Ms. Feinstein’s bill — which, unlike the 1994 assault weapons ban, would not expire after being enacted — would also ban certain characteristics of guns that make them more lethal. More than 900 models of guns would be exempt for hunting and sporting.

Such a measure is vehemently opposed by the N.R.A. and many Republican lawmakers, as well as some Democrats. “I don’t think you should have restrictions on clips,” said Senator Tom Coburn of Oklahoma, who has said he welcomes a Senate debate on guns. “The Second Amendment wasn’t written so you can go hunting, it was to create a force to balance a tyrannical force here.”

Proponents of the ban argue that in spite of claims to the contrary, the 1994 measure, of which Ms. Feinstein was a chief sponsor, helped curb gun violence. “The original bill, though flawed, had a definite impact on the number of these weapons faced by the police on streets and used in crimes,” said Adam Eisgrau, who helped write the 1994 ban while serving as Judiciary Committee counsel to Ms. Feinstein. The new bill, with more explicit language on the types of features on banned weapons, “is far more respectful of firearms for recreation uses,” he said.

Bans on assault weapons and high-capacity magazines were among the proposals unveiled by President Obama and Vice President Joseph R. Biden Jr. last week. Mr. Biden took the campaign for tougher gun laws to the Internet on Thursday in an online video chat that was part of an effort by the White House to build public support for its guns package. Mr. Biden, who developed the plans embraced by Mr. Obama, will host a round-table event in Richmond, Va., on Friday, and officials have said that Mr. Obama will travel at some point to promote the package.