US lawmakers were not told in advance of the attack ordered by President Donald Trump that killed a top Iranian military commander, a senior House Democrat said late on Thursday.

General Qassim Soleimani, head of Iran's elite Quds Force, was killed in a US airstrike alongside top Iraqi militia commander Abu Mahdi al-Muhandis early on Friday.

The high-profile assassinations are likely to be a massive blow to Iran, which has been locked in a long conflict with the United States that escalated sharply last week with the storming of the US embassy in Iraq.

While Republicans cheered news of Soleimani's demise, Democrats said there were legal concerns over the operation and warned of severe repercussions.

The strike conducted in Iraq "went forward with no notification or consultation with Congress," House Foreign Affairs Committee chairman Eliot Engel said in a statement.

Soleimani was "the mastermind of immense violence" who has "the blood of Americans on his hands," the Democratic lawmaker said.