Defence Minister Lorenzo Guerini had a "frank and articulate" phone call with US Defence Secretary Mark Esper about the situation in Iraq, his ministry said in a statement.

Esper hailed "as a strong positive signal the Italian decision to maintain its presence in the field, in the same Iraqi territory," the statement said.

Italian media quoted military sources as saying that "a few dozen" Italian soldiers had been moved from an operations centre near the US embassy in Baghdad after repeated mortar attacks.

US and allied foreign troops in Iraq are concerned they might be targeted by Iran or allied Iraqi militias in retaliation for Friday's killing in Baghdad of Revolutionary Guards General Qasem Soleimani, who commanded Iran's operations across the Middle East.

NATO announced on Saturday that it had suspended its training mission in Iraq, which fields 500 instructors.

Canada and Germany have said they are moving some troops out of the country, while France has said it has no plans to pull any of its forces.

Guerini appealed to the US for "moderation, dialogue and the sense of responsibility with which the complexity of the current situation in Iraq must be managed."

"With around 1,000 men in Iraq, over 1,000 in Lebanon in the UNIFIL (peacekeeping) mission, and just under 1,000 in Afghanistan, Italy is among the countries most committed to the stability of the region," Guerini said.

Italy has over 900 troops in and around Iraq, including 300 in Kuwait, around 450 training Kurdish fighters in Erbil, 90 in Kirkuk and 50 in Baghdad, according to Italian media.

Guerini stressed the importance of "facing future developments in a coordinated manner, with the objective of being able to continue the commitment of the Anti-Daesh Coalition, within a security framework for our military."

Daesh is an Arabic acronym for the Islamic State jihadist group.

Esper tweeted his thanks to Italy for its "important" decision which "demonstrates Italian resolve and a commitment to Iraqi stability".