The strikes came hours after Iran launched missiles at a US military facility in Qatar --the largest US military facility in the Middle East -- in retaliation for the American bombing of Tehran's nuclear facilities.

The first attack hit a radar system at the Taji base, north of Baghdad, a security source told AFP, requesting anonymity because he is not allowed to speak to the media.

A few hours later, the security source told AFP "a drone targeted... the radar system at the Imam Ali airbase" in Dhi Qar province in southern Iraq.

Another drone fell in the Radwaniya district, ten kilometres west of Baghdad International Airport, the source added, where US troops are deployed in a base as part of an anti-jihadists coalition.

"An unidentified drone struck the radar" at Taji,said government security spokesman Saad Maan, adding that another drone "fell near a generator", without providing further details.

The attacks caused material damage but no casualties were reported, Lieutenant General Walid al-Tamimi told the official Iraqi News Agency.

The Taji base hosted US troops several years ago and was a frequent target of rocket attacks.

Nobody has claimed responsibility for the attacks.

- Regional tensions -

Israel and Iran had been swapping missile fire since Israel carried out surprise strikes against Iran on June 13, prompting fears of a regional conflict.

The United States joined its ally Israel's military campaign against Iran, attacking an underground uranium enrichment centre with massive bunker-busting bombs and hitting two other nuclear facilities overnight Saturday into Sunday

A source close to the Iran-backed Iraqi factions, who had in previous years hit bases hosting US troops, told AFP "of course" the groups have nothing to do with the drone attacks.

Iraqi security sources told AFP after the Iranian strikes that "so far" Tehran had not attacked bases hosting US troops, who are deployed in Iraq as part of an anti-jihadists coalition.

The Israel-Iran conflict has forced Iraq to close its airspace.

Since the start of the war, Baghdad has been working diplomatic channels to prevent the latest violence from spreading onto its turf.

It has called on Washington to prevent Israeli jets from using Iraqi airspace to carry out attacks against Iran.

It also asked Iran not to strike US targets in its territory, according to a senior security official.

After Tehran struck the US base in Qatar, Iran's foreign minister Abbas Araghchi said his country did not intend to continue its strikes if Israel stopped its attacks, hours after Trump announced a staggered ceasefire to bring about an "official end" to their conflict.