"The American army killed them and it will pay the price," the Iran-backed head of the Lebanese Shiite group Hassan Nasrallah warned in a televised speech following Friday's strike in the Iraqi capital.

"The only just punishment is (to target) American military presence in the region: US military bases, US warships, each and every officer and soldier in the region," Nasrallah said.

He added however that American civilians such as "businessmen, engineers, journalists and doctors" should be spared.

"When the coffins of American soldiers and officers... start to return to the United States, (US President Donald) Trump and his administration will realise they have lost the region," he said.

Soleimani and top Iraqi military figure Abu Mahdi al-Muhandis were killed in a US drone strike Friday near Baghdad airport, sparking fury in Iran and Iraq.

Nasrallah's speech was beamed to black-clad supporters gathered in southern Beirut, who waved Hezbollah's yellow flag or held up portraits of Soleimani and Muhandis.

Nasrallah also called on Iraq to free itself of the American "occupation".

"Our demand, our hope from our brothers in the Iraqi parliament is... to adopt a law that demands American forces withdraw from Iraq," he said.

Iraq's parliament urged the government on Sunday to end the presence of US-led coalition forces in the country, outraged by the American strike.

Some 5,200 US soldiers are stationed across Iraqi bases to support local troops preventing a resurgence of the Islamic State jihadist group.

They are deployed as part of the broader international coalition, invited by the Iraqi government in 2014 to help fight IS.

Hezbollah is the only side not to have disarmed after Lebanon's 1975-1990 civil war.

The United States has designated it a "terrorist" group and several of its figures are under sanctions, but the party is also a key player in Lebanese politics.