The strike outside Baghdad airport killed top Iranian commander Qasem Soleimani and the deputy chief of Iraq's pro-Iran paramilitary organisation, Abu Mahdi al-Muhandis.

Syria is "certain that this cowardly US aggression... will only strengthen determination to follow in the path of the resistance's martyred leaders," a foreign ministry official was quoted as saying by the state news agency SANA.

The official described the killings as "a serious escalation of the situation" in the region and accused the United States of resorting to "the methods of criminal gangs".

The unnamed official said the strike was "part of the (US) policy aiming to create tensions and fuel conflict in countries in the region."

Soleimani had been a key backer of President Bashar al-Assad and helped him save his position after an uprising that began in 2011 threatened to topple his regime.

He was Iran's pointman in organising Iranian forces and their Shiite-dominated foreign proxies on the Syrian battlefield and a frequent visitor to Damascus.

Leaders of Syrian opposition groups for their part hailed the death of a man they blame for thousands for thousands of deaths in the nearly nine-year-old civil war.

"The murder of Qasem Soleimani, the number one perpetrator of Revolutionary Guards' crimes against the people of Syria and Iraq, is a blow that confirms that the world is able to stop Iran and protect Syrian civilians if it wants to," Nasr Hariri, a senior political opposition leader, said.

Ahmed Ramadan, another senior opposition figure, also praised the US strike.

"The killer of Syria's children has been killed, the killer of Iraq's free people has been killed," he said in a post on social media.