Security in Saudi Arabia is "under control", the kingdom's crown prince, who led a previous crackdown on al-Qaida, said Sunday after the Islamic State group claimed a fatal mosque attack.

"Incidents such as this will not destabilize us. We have been through bigger ones," said Crown Prince Mohammed bin Nayef, who is also the interior minister.

"Thank God the situation is under control. And if something happens, we will deal with it when the time comes."

He was quoted by the official Saudi Press Agency as speaking to foreign ambassadors.

In a statement carried by jihadist accounts on Twitter, IS said it was responsible for Friday's suicide blast which killed three people and wounded four outside the al-Anoud mosque in Dammam city, on the Gulf coast.

The attack came exactly seven days after IS claimed a suicide blast at another Shiite mosque, in the nearby community of Kudeih.

That bombing killed 21 people and wounded dozens in the Sunni-dominated kingdom's Eastern Province, where most of the minority Shiite community live.

IS, which considers Shiites to be heretics, has declared a "caliphate" in parts of Iraq and Syria it controls. The group has claimed numerous atrocities including the beheading of foreign hostages.

Crown Prince Mohammed has spent years in Saudi Arabia's interior ministry, personally overseeing the crackdown on al-Qaida which waged a campaign of shootings and bombings that killed foreigners and Saudi security personnel between 2003 and 2007.

A funeral for the latest bombing victims could be held Monday or Tuesday, an area resident said.