Republicans and Democrats alike expressed broad support for the toning down of sabre-rattling rhetoric both by President Donald Trump and Iranian officials, and satisfaction that no Americans were killed in Tehran's missile strike aimed at bases in Iraq housing US troops.

But classified briefings by senior administration officials left many Democrats -- and at least one angry Republican -- unconvinced about Trump's justification for killing top Iranian commander Qasem Soleimani last week while the powerful general was in Iraq, a move that sent tensions soaring.

"Our concerns were not addressed by the president's insufficient War Powers Act notification and by the administration's briefing today" by Defense Secretary Mark Esper and other top officials, House Speaker Nancy Pelosi said.

The top Democrat in Congress announced the chamber will vote Thursday on legislation aimed at preventing Trump from waging war with Iran.

"The president has made clear that he does not have a coherent strategy to keep the American people safe, achieve de-escalation with Iran and ensure stability in the region," Pelosi said in a statement.

Under the 1973 War Powers Act, the administration needs to notify Congress on major military actions but Trump, unusually, has kept classified his rationale for the strike that killed Soleimani.

"We're told it was an imminent threat" by Soleimani's forces against Americans, House Foreign Affairs Committee chairman Eliot Engel told reporters after being briefed. "I'm not sure I'm convinced about that."

Democratic presidential candidate Senator Elizabeth Warren also expressed doubts about the justification offered for killing Soleimani.

"There were so many important questions that they did not answer (and) we did not see a satisfying plan for the future," said Senate Minority Leader Chuck Schumer, irate that Esper and company "walked out" of the briefing when questioning got tough.

Several Republicans described the briefings as helpful, and said they showed intelligence pointing to Iranian attacks expected within days against Americans.

Democrats seethed over Trump's unilateral order to kill Soleimani without congressional consent. But they joined Republicans including Senator Lindsey Graham in taking heart that Washington and Tehran appeared to choose de-escalation rather than war posturing.

"In my view, retaliation for the sake of retaliation is not necessary at this time," tweeted Graham, a hawkish Trump loyalist.

But he also lashed out at concerned Democrats, saying "I find this whole idea that somehow the national security team did not have a good basis to hit this guy to be ridiculous."

The briefings left not just Democrats fuming. Senator Mike Lee said it was "insulting" how briefers restricted questions about the appropriateness of military intervention with Iran.

Lee called the briefers' behavior "un-American," and announced he would support a Democratic-led war powers resolution.

Tensions between the US and Iran have escalated in recent years, but they spiked when Soleimani was killed. Iran retaliated this week by firing missiles at Iraqi bases where US troops are stationed.

Trump said he sought peace and that Iran appeared to be "standing down," while Tehran signalled it did not seek further confrontation.

"Both sides have said that that's their objective," senior House Democrat Steny Hoyer said. "Our hope is that that is what happens."