Vice President Joseph R. Biden said Tuesday the fight for congressional action on gun legislation is far from over while outlining unilateral steps the Obama administration has taken to combat gun violence in the wake of the Connecticut school shootings in December.

The address was simultaneously a summary of what President Obama has been able to do through executive actions since the shootings in Newtown, Conn., and a rallying cry to remind voters and lawmakers that neither Mr. Biden nor Mr. Obama is going to let the issue fade from public memory.

“The most important message to take from here today is the president and I are a team,” Mr. Biden said. “We have not given up. Our friends in the House and Senate, they have not given up.”

Mr. Biden said because of a “perverted” rule requiring 60 votes to herd off potential filibusters in the Senate, the 41 Republicans and four Democrats who opposed the administration’s gun control bill were able to block it even though it had the support of 51 Democrats and four Republicans.

“I know for a fact some of them wonder about, now, whether that was a prudent vote,” said Mr. Biden, who described the shooting deaths of 20 first-graders and six adults at Sandy Hook Elementary School as “the straw that broke the camel’s back” in the gun debate.

“The one thing that each of us have been saying to our colleagues about these votes is the country has changed. You will pay a price, a political price, for not getting engaged and dealing with gun safety,” he said.

However, regardless of what could have happened differently in the Senate, the administration’s gun control push always faced extremely long odds in the House and it wasn’t clear Tuesday why another push would be more popular than before in the Republican-led chamber.

Still, Mr. Biden said the administration has completed or made significant progress on 21 of the 23 executive actions Mr. Obama laid out in January, elaborating Tuesday on such specifics as the departments of Education, Justice, Homeland Security, and Health and Human Services releasing guides to schools, institutions of higher education and houses of worship on how to deal with emergencies such as active shooter situations and natural disasters.

He also said Homeland Security and Justice have expanded access to federal training on active shooter situations for law enforcement, first responders, and school officials.

The two actions still outstanding are getting a permanent director for the Bureau of Alcohol, Tobacco, Firearms and Explosives and finalizing regulations regarding “mental health parity.”

The nomination of acting ATF Director B. Todd Jones for the permanent post is pending before the Senate Judiciary Committee, and an administration official said it has moved on the mental health regulations but they haven’t taken effect because of required public-comment periods.

Shortly after Mr. Biden’s remarks, Connecticut’s two Democratic Senators, Richard Blumenthal and Christopher Murphy, commended the administration but pushed for more.

“These steps are important, but the administration knows there is no substitute whatsoever for legislation,” Mr. Blumenthal said. “Congress has been complicit by its inaction.”

The failed measure co-sponsored by Sens. Joe Manchin III, West Virginia Democrat, and Patrick J. Toomey, Pennsylvania Republican, that failed in April would have expanded background checks to firearms sales online and at gun shows. Right now, only federally licensed dealers are required to perform the checks.

Mr. Murphy said that they are in discussions with about a half-dozen senators regarding slightly amended legislation, but he stressed that pressure on lawmakers would have to come from senators’ constituents and the American public, not the White House.

He said they will not make major changes to the Manchin-Toomey measure, but would entertain slight changes on a rural exemption for the checks — an idea that had been bandied about during negotiations earlier in the year.

Other changes could include a clarification that no national record-keeping will result from the bill and other mental health features, “but there will be absolutely no hollowing out of this bill,” Mr. Blumenthal said. “We are not going to weaken what a majority of senators have already said they want and 90 percent of the American people say we need, and there can be changes to accommodate senators who feel that they need some changes in the bill without weakening it.”

Mr. Murphy said the definition of “rural” was still being worked out, but would likely be a very small number of extremely rural areas, mostly in the western part of the country.

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