Iraqi Prime Minister Mohammed Shia Al Sudani landed in Kuwait on Wednesday for an official visit.
Mr Al Sudani, who took office last month, is seeking to assure Iraq's neighbours that his Iran-backed government will continue to strengthen ties.
The Iraqi leader has the support of the largest parliamentary group, the Co-ordination Framework, which is made up of Shiite militias and political parties close to Iran.
He was greeted by Kuwait’s Prime Minister Sheikh Ahmad Nawaf Al Sabah, his office said. They are set to discuss relations between the two nations and ways to enhance co-operation, an Iraqi statement said.
On Monday, he discussed bilateral relations with Jordan's King Abdullah II in Amman. King Abdullah said Iraq has an important role to play in the Arab world.
In August 1990, Saddam Hussein ordered his army into Kuwait to seize what he described as “Iraq's 19th province”, before being pushed back seven months later by a US-led coalition.
Since the 2003 US-led invasion of Iraq that toppled Saddam, diplomatic relations and co-operation have resumed. Kuwait sent its ambassador to Baghdad in 2008.
Earlier this year, Iraq made the final payment for the $52.4 billion of claims for the damages during the invasion.
But there are challenging issues still at play between the two nations.
Iraqi fishermen complain of harassment by Kuwaitis who maintain that the fishermen do not respect boundaries. Iraqi officials in charge of building the multibillion-dollar Al Faw Port project on the Gulf often complain about the same harassment.
Iraq’s mainly Sunni neighbours have sought since 2007 to restore ties damaged by Saddam’s rule and the 2003 invasion as the security situation in Iraq has improved.
Washington has also pressed for Arab countries to play a bigger political role in Iraq, partly to counter Iranian influence and to promote reconciliation between Iraq’s minority Sunni community and majority Shiites.
Iraqi PM visit to Jordan — In pictures
