A suicide bomber blew himself up at a packed Shi'ite Muslim mosque in Kuwait city during Friday prayers, killing more than ten people, the governor of Kuwait City said.

The Islamic State militant group claimed responsibility for the attack in a statement posted on social media and said it targeted a "temple of the rejectionists" - a term it usually uses to refer to Shi'ite Muslims, whom it regards as heretics.

It was the first suicide bombing attack on a Shi'ite mosque in the small Gulf Arab oil exporter, where Sunnis and Shi'ites live side by side with little apparent friction.

Islamic State on Tuesday urged its followers to step up attacks during the Ramadan fasting month against Christians, Shi'ites and Sunni Muslims fighting with a US-led coalition against the ultra-radical group.

Kuwaiti parliament member Khalil al-Salih said worshippers were kneeling in prayer when a suicide bomber walked into the Imam al-Sadeq Mosque side and blew himself up, destroying walls and the ceiling.

"It was obvious from the suicide bomber's body that he was young. He walked into the prayer hall during sujood (kneeling in prayer), he looked ...in his 20s, I saw him with my own eyes," he told Reuters by telephone.

"The explosion was really hard. The ceiling and wall got destroyed," he said, adding that more than 2,000 people from the Shi'ite Ja'afari sect were praying at the mosque.

ATTACKS

Kuwaiti television showed footage of the emir, Sheikh Sabah al-Ahmed al-Sabah, visiting the damaged mosque in the eastern Sawaber district.

The Interior Ministry told citizens to stay away from the scene to allow authorities to investigate.

Kuwait City governor Thabet al-Muhanna said at least 10 people were killed in the attack.

Islamic State has recently twice targeted Shi'ite mosques in neighbouring Saudi Arabia and carried out attacks against members of the sect's Zaydi branch in Yemen.

Kuwait's Minister of Justice, Awqaf and Islamic Affairs Yaqoub Al-Sanea condemned the "terrorist attack" which he said "threatens our security, and aims to fracture the country's unity," KUNA said.

"Kuwait will remain an oasis of security for all groups of Kuwaiti society and all sects. The government is taking many procedures to protect prayers and mosques."