WASHINGTON — Under increasing pressure to defend the killing of a top Iranian general in Iraq, senior Trump administration officials offered new justifications but little detail on Tuesday, citing threats to the American Embassy in Baghdad and intelligence suggesting other imminent attacks that helped prompt the strike.

Democrats stepped up their criticism of intelligence that the administration provided immediately after the drone strike last week that killed Maj. Gen. Qassim Suleimani, the leader of Iran’s Islamic Revolutionary Guards Corps. The administration’s formal notification to Congress, which remains classified, provided no information on future threats or the imminent attack, officials who have read it said.

Several said it was improperly classified, and Senator Richard Blumenthal, Democrat of Connecticut, called it “vague and unacceptably unspecific.” Lawmakers pressed for more answers on Tuesday at an intelligence briefing by administration officials.

Iranian forces or their proxies were days from attacking American personnel when President Trump decided to strike General Suleimani, Defense Secretary Mark T. Esper told reporters at the Pentagon. Mr. Esper added that General Suleimani had traveled to Baghdad to coordinate attacks following up on a two-day siege of the United States Embassy there last week by pro-Iranian demonstrators. He declined to elaborate but called the intelligence “exquisite.”