The comments are likely to fuel U.S. concerns over Moscow's growing influence in the Middle East as Russia bombs Islamic State targets in neighboring Syria and shares intelligence with Iraq under a new regional security agreement.
"We are looking forward to seeing Russian war planes bomb the positions and headquarters of Daesh [Islamic State] in Iraq and all its joint supply routes with Syria," Muen Kadhimi, a senior aide to the leader of the Badr Brigade, told Reuters.
"We will strongly welcome such intervention by the Russians to take out Daesh in Iraq."
The United States has led airstrikes against Islamic State in Iraq for more than a year, but Baghdad has repeatedly called for greater engagement and air support for Iraqi forces trying to regain territory against the militant group.
Earlier on Monday, the Shi'ite Asaib Ahl Haq force also said it fully supported Russia's intervention against Islamic State in the Middle East. Spokesman Naim Uboudi said Russia's airstrikes in Syria had already produced results.
"We know that the United States, during the past year and a half, was not serious about putting an end to Daesh … they attempt to manage the crisis rather than put an end to it."
Support for Russian action against Islamic State in Iraq from the country's Shi'ite militias is seen as critical before any airstrikes are possible.
Firmly backed by Tehran, the militias are far more influential than the Iraqi army or security forces, who have proven ineffective against Islamic State, which controls about one third of Iraq and large swathes of neighboring Syria.
Iraqi Prime Minister Haider Abadi has also said Baghdad would welcome Russian air strikes against Islamic State in his country on Iraqi soil.Last month, Iraq said its military officials were engaged in intelligence and security cooperation in Baghdad with Russia, Iran and Syria to counter the threat from Islamic State.