Iranian ambassador to Kuwait Alireza Enayati in a meeting with Kuwaiti foreign minister Sabah Al Khalid Al Sabah delivered Rouhani’s letter addressed to Kuwait's ruler, Sheikh Sabah Al Ahmad Al-Jaber Al-Sabah.
Several officials of Kuwaiti foreign ministry had also attended this meeting.
In January, Kuwait's foreign minister paid a rare visit to Tehran. He delivered a message from the emir to Rouhani, describing a "basis of dialogue" between Persian Gulf Arab states and Iran.
Rouhani replied to the message in the letter delivered by Iran's ambassador on Monday.
Rouhani visited Oman and Kuwait in February on his first visit to the Persian Gulf states since taking power in 2013.