Pointing to Iran's assistance for regional nations in the fight against terrorism, President Rouhani said Iran will definitely keep offering help to any country requesting assistance in the war on terrorism.
Rouhani will travel to Kuwait later on Wednesday for talks with the country's emir, Sheikh Sabah al-Ahmad al-Sabah.
Talks between the two leaders are expected to tackle bilateral relations and regional and worldwide developments, the official said Tuesday on condition of anonymity due to restrictions on speaking to media.
They also held talks on "latest regional and worldwide developments", said the statement, without giving further details.
As part of a one-day tour on Wednesday, Rouhani is visiting Oman and Kuwait, two countries Iran has enjoyed relatively warmer relations with in comparison to its ties with regional powerhouse Saudi Arabia.
"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.
While Iran has supported Bashar al Assad's regime in Syria and Shiite Houthi rebels in Yemen, the Arab Gulf states - namely Saudi Arabia, the United Arab Emirates and Qatar - have supported the Syrian opposition as well as the Yemeni President Abdrabbuh Mansour Hadi's embattled government.
Turkish shelling kills 60 civilians in Syria's al-Bab
Al-Bab has been under IS control since 2014, when the group seized large swathes of territory in Syria and neighbouring Iraq, proclaiming its self-described caliphate.
Iranian President Hassan Rouhani said that Iran welcomes deepening ties with the European Union members in all spheres.
He also appealed for a ceasefire, increased humanitarian aid and political dialogue to resolve the conflict in Yemen. Kuwait, which has a significant minority, has sought to maintain relations with Iran.
"There are now good conditions for developing and consolidating relations between Iran and Oman", Rouhani said, calling for stronger economic ties.
Rouhani said in January that at least 10 countries including Kuwait have offered to mediate in the escalating feud between Saudi Arabia and Iran.
The GCC member states often accuse Iran of meddling in their internal affairs - claims denied by Tehran.
Tension has mounted between the Gulf and Iran since Saudi Arabia cut diplomatic ties with Tehran early past year after two Saudi diplomatic missions in Iran were attacked by protesters following Riyadh's execution of a prominent Shia cleric.