WASHINGTON — Pittsburgh Mayor Bill Peduto said he pressed senior White House officials and Republican lawmakers to pass a “total package” of gun legislation that includes both background checks and a red flag law, while signaling compromise on some hurdles that, even after a wave of mass shootings, have blocked gun control efforts in Congress.

Mr. Peduto, who on Tuesday joined a delegation of mayors from cities that have suffered such tragedies, said he hopes to turn a grim coalition into a political force in Washington.

“There seems to be a critical point we’re at right now that requires a bipartisan effort of mayors across the country,” Mr. Peduto said in an interview outside the U.S. Capitol.

“There’s a place for Pittsburgh in this discussion that comes from our history of being pragmatic and getting things done,” he said. “Washington has lost both of those. Hopefully, with the infusion of mayors in this discussion, they can get it back.”