A top Iranian diplomat has said his country is open to resolving differences with its Gulf rivals, Saudi Arabia and the United Arab Emirates, "as quickly as possible".

Tehran's ambassador to Iraq, Iraj Masjedi, said in remarks published on Tuesday that his government "welcomes efforts to resolve issues either from inside Iraq or any other country in the region".

Masjedi said top Iranian commander, Qassem Soleimani, killed at Baghdad airport in a US air raid last month, was carrying a message setting out Iran's position on possible rapprochement with Saudi Arabia, the Iraqi state news agency reported.

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"Tehran welcomes Iraq's role in trying to solve differences between Iran and Saudi," Masjedi was quoted as saying, referring to recent efforts by Iraq to mediate between the regional rivals.

He said Iran wished "to resolve differences and challenges" with its rivals "as soon as possible". The official made his remarks during an interview with the agency, which published its excerpts in Arabic.

Shia Muslim Iran has long been at odds with Sunni Arab states in the Gulf, which are also allies of the United States.

Washington blamed a series of attacks against oil interests in the Gulf last year on Iran, and the killing of Soleimani brought the region to the brink of war.

Soleimani's message that he was meant to deliver when he arrived in Baghdad on January 3, the day he was killed, set out Tehran's position on "fighting terrorism and achieving peace and security in the region," Masjedi said.

Last month, a senior Saudi official said he was not aware of any message carried by Soleimani for mediation efforts between Riyadh and Tehran.

'Dismantle' US bases

The killing of Soleimani struck a blow to Iran's regional strategy. Soleimani was the mastermind behind Iran's control, through proxy militia forces and political alliances, over a corridor of territory stretching from Tehran through Iraq to the Mediterranean via Syria and Lebanon.

Washington says it is determined to counter Iran's influence in the region and has imposed economic sanctions on the Islamic republic's oil sector and targeted its paramilitary forces.

After Soleimani's killing alongside top Iraqi paramilitary commander Abu Mahdi al-Muhandis, Iran launched at least 15 missiles at two bases hosting US forces in Iraq, causing traumatic brain injury to 50 US service members but no deaths.

Masjedi said the attack on the sprawling Ain al-Assad base was in response to Washington using "bases in the region ... and choosing Iraqi territory" to kill Soleimani - a suggestion that the drone attack was launched from Ain al-Assad.

He said Iran would respond harshly to any future US attack.

"If we wanted to put a limit on such events unfolding again, the US must stop intervening in the region's issues, and must dismantle its bases that are used to carry out such terrorist behaviours," Masjedi said.

Separately, he also welcomed the naming last week of Iraq's Prime Minister Mohammed Tawfiq Allawi, who is accepted by Iran-backed Iraqi political groups, but rejected by protesters who have staged months of anti-establishment demonstrations.