Rouhani held talks with Kuwait's Emir Sheikh Sabah al-Ahmad Al-Sabah, who last month launched a dialogue with the Islamic republic to normalise Iran-Gulf relations.
An official statement cited by the KUNA news agency said they discussed bolstering bilateral ties in all fields.
They also held talks on "latest regional and international developments," said the statement, without giving further details.
Ahead of his visit to Oman and Kuwait, Rouhani had expressed support for the latter's efforts to "resolve misunderstandings and boost relations" with Gulf countries.
"In this trip, there will be discussions about the region, the situation in Iraq, Syria and in particular in Yemen," Iran's official news agency IRNA quoted him as saying.
Rouhani's tour excludes regional kingpin Saudi Arabia, Iran's key rival.
Tehran's ties with other Gulf states have been strained over its support for the Syrian regime of Bashar Al-Assad and alleged backing of Yemen's Huthi rebels.
Rouhani was welcomed by Sultan Qaboos in Muscat, where the two discussed bilateral relations and the situation in the region, Oman's official ONA news agency reported.
"Tehran has always been in favour of resolving problems and disputes through dialogue," Rouhani said, according to Iranian media.
"Iran's military power is only defensive."
He appealed for a ceasefire, increased humanitarian aid and political dialogue to resolve the conflict in Yemen.
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"Today, the Yemenis are in a particularly disastrous situation and we all have to act as Muslim countries to help this people," he said.
Iran traditionally maintains good relations with Oman, with which it shares control of the key Strait of Hormuz shipping lane.
"There are now good conditions for developing and consolidating relations between Iran and Oman," Rouhani said, calling for stronger economic ties.
GULF DIALOGUE HOPES
Kuwaiti Foreign Minister Sheikh Sabah Khaled Al-Sabah visited Tehran last month, calling for a "normalisation of ties and opening dialogue".
His deputy, Khaled al-Jarallah, said in remarks published Wednesday that he hopes Rouhani's visit would lead to a dialogue between the Gulf states and Iran.
The elements needed for the dialogue, which were included in the emir's letter, call for non-interference in the internal affairs of the Gulf states, respecting their sovereignty and establishing good neighbouring relations, Jarallah said in the comments published in Kuwait's Al-Qabas newspaper.
The Gulf Cooperation Council (GCC) summit held in Manama in December asked Kuwait to initiate contacts with Tehran to start a dialogue to improve ties.
Kuwait, where 30 percent of native citizens are Shiites, has maintained normal relations with Tehran despite taking part in the Saudi-led military campaign on Yemen's Shiite Huthi rebels.
Iran has had no diplomatic relations with Saudi Arabia since January 2016, when demonstrators stormed the kingdom's missions in Tehran and Mashhad in protest at the execution of a Saudi Shiite Muslim cleric.
Ties were already strained between the region's leading Shiite and Sunni powers, which have taken opposing sides in the conflicts in Syria and Yemen.
Oman, which has a significant Shiite minority, has historically had good ties with Iran, with which it shares control of the Strait of Hormuz.
The sultanate is the only one of the six Gulf Arab states not taking part in the Saudi-led military intervention against the Huthis in Yemen.