Iranian president Rouhani was also in Oman last week where he said he sought good relations with his Gulf neighbors
Shaikh Sabah will discuss ways to enhance cooperation between the two countries with Sultan Qaboos Bin Saeed.
During his visit to the Sultanate, the Emir of Kuwait will be accompanied by a high-ranking official delegation.
Last Wednesday, Iranian President Hassan Rouhani was on an official visit to Oman before he headed to Kuwait.
Ahead of his visit Rouhani said his country sought good relations with its Gulf Arab neighbours.
Relations between Iran and the Arab countries of the Gulf, particularly Saudi Arabia, remain strained over their support for opposing sides in the conflicts in Syria and Yemen.
Rouhani also said there should be greater unity between Shiites and Sunnis, saying they had “coexisted side by side peacefully for hundreds of years”, Irna reported.
On Sunday, Saudi Arabia’s Foreign Minister Adel Al Jubeir rejected Iranian calls for dialogue saying Tehran was the main sponsor of terrorism in the world, a destabilising force in the Middle East and wanted to “destroy us.”
“Iran remains the single main sponsor of terrorism in the world,” Al Jubeir told delegates at the Munich Security Conference.
“It’s determined to upend the order in Middle East … [and] until and unless Iran changes its behaviour it would be very difficult to deal with a country like this.”
Al Jubeir said Iran was propping up the government of Syrian President Bashar Al Assad, funding Al Houthi militants in Yemen and violent groups across the region.
He said the international community needed to set clear “red lines” to halt Iran’s actions.