Iraqi Shiite lawmakers and militia leaders are urging Russia to launch airstrikes on Islamic State militants in their country, a sharp reproach to the U.S.-led air campaign targeting the extremist group.

Since Moscow began bombing opponents of the regime in Syria last week, the lawmakers and militia leaders have pressed Prime Minister Haider al-Abadi to invite Russia to intervene in Iraq. Mr. Abadi said last week that he would welcome Russian airstrikes in Iraq as long as they were coordinated with the U.S.-led coalition.

Iraq’s Shiite politicians, who dominate the government, were largely united in their praise of Russia’s intervention and calls for Russian airstrikes.

“We welcome Russian airstrikes in Iraq to help hit Islamic State headquarters, target Islamic State supply lines from Syria and target the oil smuggling lines,” said Moeen al-Kadhimi, a spokesman for the Badr Corps, an Iranian-backed militia and political party that plays a front-line role in fighting Islamic State. “We welcome Russia as they have advanced military technology and can help with intelligence.”