Before leaving Tehran Rouhani hailed the "special" relations between Iran and Iraq, saying they could not be compared to Baghdad's ties "with an aggressor country like America".

His visit to Iraq is the first since he became president in 2013.

"Iran-Iraq relations are special," Rouhani said at Tehran's Mehrabad airport before flying to Baghdad, Iranian state television reported, adding that Tehran was always ready to help its neighbours.

"America is despised in the region. The bombs that the Americans dropped on Iraqis, Syrian people and other countries cannot be forgotten," he added.

Baghdad has been under pressure from Washington to limit ties with its neighbour, particularly after the United States last year withdrew from the 2015 nuclear deal with Iran and hit Tehran with sanctions.

Iraq was given limited waivers to continue buying electricity and natural gas from Iran, with Washington calling on Baghdad to partner with US companies to become energy independent.

After Turkey, Iran is the top supplier of imported goods to Iraq, including cars, gas, home appliances and vegetables.

Iran has close but complicated relations with Iraq, with significant influence among its Shiite political groups.

The two countries fought a bloody war from 1980 to 1988 and Tehran's influence in Baghdad grew after the 2003 US-led invasion of Iraq toppled the government of Saddam Hussein.

Iran was the first country to respond to Iraqi calls for help after Islamic State group jihadists captured second city Mosul in 2014 and threatened to overrun Baghdad and Kirkuk.

Tehran dispatched "military advisors" and equipment overnight along with the famous Revolutionary Guards elite Quds Force commander Qasem Soleimani to prevent IS jihadists from approaching its western borders.

Following the defeat of IS in Iraq, Iran is trying to position itself to gain a prime role in rebuilding the war-ravaged country.

During the visit, Rouhani is set to meet Iraqi Prime Minister Adel Abdel Mahdi and President Barham Saleh, as well as the country's chief Shiite cleric Grand Ayatollah Ali Sistani, according to the Iranian government's website.

Iranian Foreign Minister Mohammad Javad Zarif preceded Rouhani to Iraq to prepare for the visit.