Hadi Al Amiri delivers a speech on Russia's military intervention in Syria in the southern Iraqi city of Najaf.
Najaf - Hadi Al Ameri Baghdad had turned to Russia because the US-led coalition was not serious about fighting the Daesh.
A top leader of Iraq's Popular Mobilisation paramilitary organisation said on Monday that Baghdad had turned to Russia because the US-led coalition was not serious about fighting the Daesh group.
"To this day, we have not seen a really serious effort to fight Daesh," Hadi Al Ameri said in the holy city of Najaf.
"There are some who try to contain Daesh but not really eliminate them and prevent those fighters from returning to Europe, which is where they came from," he said.
Ameri is a key MP of the Badr movement, a Tehran-backed Shia party which also has a powerful military wing. He was speaking at a conference organised by Badr's TV channel Al Ghadeer.
"This lack of seriousness of the international coalition made us change tack. Russia is moving in a very serious way against Daesh," he said.
Russia's airforce began air strikes in Syria last week.
Moscow says it has been targeting Daesh but Washington and its allies say Russia does not distinguish between Daesh and other groups and accuses the Kremlin of being focused on protecting Syrian President Bashar Al Assad and his regime.
Iraq announced last week it had agreed to set up a cell in Baghdad aimed at increasing intelligence cooperation with Russia, Syria and Iran in the fight against Daesh.
The government in Baghdad has since said it might consider allowing Russia to bomb Daesh targets in Iraq as well.
Ameri said Daesh's ability to recruit internationally was unprecedented in the history of terrorism.
"They are currently recruiting fighters from 108 countries in the world and all of them are going through Turkey, with the coalition's knowledge," he said.
"We told America" 'if you are serious about fighting Daesh, you have to stop those arrivals, which are wreaking carnage and destruction on Syria and Iraq'," he said.
The US-led coalition - which also includes France and Britain - has carried out more than 7,000 strikes on Iraq and Syria since August 2014.
Those have helped Iraqi forces roll back some of the territorial gains Daesh made last year but the militant group has proved resilient and the security forces slow to reform.
Ameri and other Iraqi politicians have criticised the West's commitment as conditional and arms deliveries as too slow.