Iraqi premier in Iran after recent visits to Turkey, Jordan and Saudi Arabia

Iraqi Prime Minister Haider al-Abadi is in Iran after recent stops in Turkey, Jordan, and meetings with US officials and allies eager to pull Baghdad into their political orbit.

He first attended an official reception at a government estate north of Tehran and is meeting with Senior Vice President Eshaq Jahangiri on Thursday.

Iran remains a major player in the war against the Islamic State group and culturally across Iraq, its one-time bitter enemy when Iraqi dictator Saddam Hussein waged an eight year war on Iran in 1980s that left more than one million casualties on both sides.

Abadi visited Iran's regional rival Saudi Arabia on Saturday, amid warming ties with Riyadh.

Saudi Arabia is also seeking to counter Iranian influence in Iraq.

After years of tense relations, ties between Sunni-ruled Saudi Arabia and Shia-majority Iraq have begun looking up in recent months.

After former dictator Saddam Hussein's August 1990 invasion of Kuwait, Riyadh severed relations with Baghdad and closed its border posts with its northern neighbour.

Ties remained strained even after Saddam's overthrow in the 2003 US-led invasion of Iraq, since when successive Shia-dominated governments in Baghdad have stayed close to Tehran.

But a flurry of visits between the two countries this year appears to indicate a thawing of ties.