Tensions have risen between predominantly Shi'ite Iran and the mainly Sunni Arab countries of the Gulf, particularly Saudi Arabia, over their support for opposing sides in the conflicts in Syria and Yemen.
Sabah Khaled al-Sabah's visit, which included delivering a written message from the emir of Kuwait to Iranian president Hassan Rouhani, appeared to be a step toward decreasing tension.
IRNA did not report any details of the message.
"It's necessary that the differing views and misunderstandings between the countries of the region should come to an end in a calm atmosphere and through frank dialogue," Sabah said, according to IRNA, a reference to Gulf Arab states who worry that Iranian influence in the region is growing at their expense.
Rouhani expressed support for improving relations in the region, based on "mutual respect, positive neighbourhood ties and Islamic brotherhood," according to IRNA.
Saudi Arabia and Bahrain in January 2016 cut diplomatic relations with Iran and some other Gulf states recalled their ambassadors in solidarity with the kingdom after its embassy in Iran was torched by protesters.
But long-standing trade links and shared access to oil and gas fields have stopped many Gulf states from shutting the door on Iran.