The attacks follow a series of operations against tankers in highly sensitive Gulf waters which the US has blamed on Iran, raising fears of a regional war.

In Baghdad, officials have voiced fears that a proxy conflict between the bitter enemies could play out in Iraq, where political and armed groups routinely accuse each other of being agents for foreign states.

On Wednesday at dawn, "a Katyusha rocket fell on an Iraqi drilling company in the Burjesiya area near Basra, wounding three people according to an initial assessment," Iraqi military command said in a statement.

Oil ministry spokesman Assem Jihad told AFP that those wounded were all Iraqis.

Burjesiya is a complex near southern Iraq's main city, in a key oil-producing region hosting various Iraqi and foreign companies including US major Exxon Mobil.

The firm withrew its 83 expatriate employees from a nearby oil field in mid-May after Washington pulled non-essential staff from its Baghdad embassy, citing threats from Iranian-linked armed groups.

The Exxon Mobil staff had since returned.

Burjesiya is several kilometres (miles) from oil wells, and the attack had "no impact on production", Jihad said.

Hours before the Burjesiya incident, the Iraqi military announced that an improvised rocket had hit a regional command base in the northern city of Mosul, where American troops are reportedly deployed.

And on Monday evening, three Katyusha rockets hit the Taji army base, which hosts both Iraqi and foreign troops, including Americans.

No group has claimed the attacks, but experts say they appear to have been fired from Shiite-majority areas north of Baghdad.

That would appear to implicate pro-Iranian Shiite armed groups, as opposed to Sunni jihadists who continue to carry out hit-and-run attacks despite the elimination of the Islamic State group's "caliphate".

An Iraqi official speaking on condition of anonymity said rocket fire had also targeted a Baghdad airbase on Monday.

On Friday evening, "three mortar rounds hit the Balad airbase (north of Baghdad), starting a fire," the same source said.

On Tuesday, Prime Minister Adel Abdel Mahdi said he had "ordered all forces to take all necessary measures" to prevent further rocket attacks.

"These actions disrupt the political situation and give a distorted picture of the security situation," he said.

Baghdad, which declared victory over IS jihadists in late 2017 after a gruelling offensive against their self-proclaimed "caliphate", has played up Iraq's return to stability as it seeks to position itself as key diplomatic actor in the region.