Attorney General William Barr has drafted a proposal to speed up executions for people convicted of mass killings, a senior White House official said Monday.

Marc Short, chief of staff for Vice President Mike Pence, told reporters that the measure to fast-track capital punishment in cases of mass killings will become part of any final package on gun legislation proposed by the White House to Congress.

Mr. Short discussed the proposal briefly on Air Force Two as the vice president was flying Monday from Poland to Ireland.

The development came two days after another mass shooting in Texas claimed the lives of seven people, in addition to the gunman, who was shot and killed by police. Authorities said the gunman had been fired from his job earlier in the day.

The Associated Press reported Monday that more than half of the perpetrators involved in mass shootings since 2006 have died during their rampages.

Congress is scheduled to return next week from a monthlong recess, and lawmakers haven’t reached a consensus on how to address gun violence.

President Trump, who has been under pressure to propose gun legislation since two mass shootings last month in Ohio and Texas, said Sunday that his administration “is committed to working with Congress to stop the menace of mass attacks.”

Unlike his previous comments after mass gun violence, Mr. Trump did not mention universal background checks as part of any solution.

“It would be wonderful to say — to say ‘eliminate,’ but we want to substantially reduce the violent crime — and actually, in any form,” Mr. Trump said. “This includes strong measures to keep weapons out of the hands of dangerous and deranged individuals, and substantial reforms to our nation’s broken mental health system. To reduce violence, we must also ensure that criminals with guns are put behind bars and kept off the streets.”

Democratic presidential front-runner Joseph R. Biden said Mr. Trump “has no intestinal fortitude to deal with this.”

Speaking to reporters while campaigning in Iowa, Mr. Biden reiterated his position on banning assault weapons and said he sees “no compromise” with Republicans in Washington.

“This is one we have to just push, push, and push,” Mr. Biden told reporters. “I’ve seen nothing [from Republicans]. The president has no intestinal fortitude to deal with this. He knows better. His instinct was to say, ‘Yeah, we’re going to do something on background checks.’ What’s he doing? Come on, this is disgraceful. This is disgraceful what’s happening.”

Shortly after mass shootings last month in El Paso, Texas, and Dayton, Ohio, that killed 31 people, Mr. Barr said he would propose legislation to expedite the death penalty for mass murderers and cop killers.

“We will be proposing legislation providing that in cases of mass murder, or in cases of murder of a law enforcement officer, there will be a timetable for judicial proceedings that will allow imposition of any death sentence without undue delay,” the attorney general told the Fraternal Order of Police convention in New Orleans on Aug. 12. “Punishment must be swift and certain.”

He said Mr. Trump “will not let acts of mass shootings and domestic terrorism go unanswered.”

“He has been consulting widely and has directed me and [FBI] Director [Christopher A.] Wray to work with our state and local partners, as well as the private sector, to develop strategies and measures to address these threats, including developing tools that can assist us in detecting potential mass shooters before they strike,” Mr. Barr said at the time. “I anticipate that we will be sharing range of proposals — legislative as well as operational — in the near future.”

The president said Sunday that he is talking with many lawmakers in the House and the Senate about proposals to reduce gun violence. He downplayed renewed calls for universal background checks on firearm purchases, saying the proposal would not have prevented any of the recent mass shootings.

“As strong as you make your background checks, they would not have stopped any of it,” the president said.

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