US Secretary of State Colin Powell has held talks with Kuwaiti Prime Minister Sheikh Sabah al-Ahmad al-Sabah on security in the region.
Powell paid an unexpected visit to the Iraqi president on Friday
They said Kuwait's role in combating terrorism and the situation in Iraq had been central to their talks.
Sheikh Sabah also said he would discuss a Saudi plan for a Muslim force in Iraq with the Iraqi interim prime minister.
Mr Powell is on a tour of the Middle East and Europe that has included a surprise visit to Baghdad.
After discussions with Iraqi President Ghazi al-Yawer on Friday, Mr Powell restated Washington's determination to stand by the Iraqi interim government.
He also promised that the US would speed up the flow of cash for reconstruction to help deal with continuing violence.
The BBC's Jill McGivering, who is accompanying Mr Powell, says the visit was seen in Baghdad as a gesture of support for an interim government facing continuing violence.
Following his meeting with President Yawer, Mr Powell said he had sent the clear message that the rate of spending on reconstruction projects would be increased sharply, employing people who wanted jobs.
Mr Powell's visit was kept a closely guarded secret right until the last minute.
On Thursday, Mr Powell met Iraqi Prime Minister Iyad Allawi in Saudi Arabia, where both gave a cautious welcome to a Saudi proposal to send Arab or Muslim forces to Iraq.
Foreign ministers from Algeria, Bahrain and Tunisia on Thursday discussed the possibility of sending troops to Iraq.
The talks in Tunis were attended by Iraqi Foreign Minister, Hoshyar Zebari, and the Arab League Secretary General Amr Moussa.
Islamic militants have threatened to retaliate against any country which contributes to the force.
The next stop on Mr Powell's itinerary is Bosnia.