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Witnesses reported a huge blast at the Imam Ali mosque in the village of al-Qadeeh, in Qatif governorate.
It is the first such incident in Saudi Arabia amid rising tension in the wider region between Sunni and Shia Muslims.
Islamic State (IS) group said it was behind a similar attack on a Shia mosque in neighbouring Yemen on Friday, which injured about a dozen people.
But it said nothing about the bombing in eastern Saudi Arabia and no other group has said it was behind the attack.
Television pictures of the Saudi bombing broadcast on Lebanon's al-Manar network showed shattered glass and debris inside the mosque, where scores were said to have been praying.
Bodies covered in sheets could be seen laid out on the floor, while injured people in bloodstained clothes were rushed out on stretchers.
Qatif hospital has issued an urgent call for blood donations and called in off-duty staff to cope with the high number of casualties.
The attack on Friday comes at a time when the Saudis are leading a coalition of Arab states in an air campaign against Shia rebels in Yemen.
Saudi Arabia has also been threatened by IS, which is being targeted by a US-led coalition including the Sunni kingdom.
In November last year, an audio recording purported to be from IS chief Abu Bakr al-Baghdadi called on Saudi followers to attack Shia targets.
More than 2,000 Saudis are believed to have joined IS, with hundreds having returned home. Saudi Arabia has launched a security crackdown in recent months, arresting hundreds of IS suspects.
At least 10 people have been killed
in a suicide bombing at a Shia mosque in Saudi Arabia's Eastern
Province, a doctor has told the BBC.
The emergency doctor at Qatif Central Hospital said at least 70 had been injured, "some very critically".Witnesses reported a huge blast at the Imam Ali mosque in the village of al-Qadeeh, in Qatif governorate.
It is the first such incident in Saudi Arabia amid rising tension in the wider region between Sunni and Shia Muslims.
Islamic State (IS) group said it was behind a similar attack on a Shia mosque in neighbouring Yemen on Friday, which injured about a dozen people.
But it said nothing about the bombing in eastern Saudi Arabia and no other group has said it was behind the attack.
Television pictures of the Saudi bombing broadcast on Lebanon's al-Manar network showed shattered glass and debris inside the mosque, where scores were said to have been praying.
Bodies covered in sheets could be seen laid out on the floor, while injured people in bloodstained clothes were rushed out on stretchers.
Qatif hospital has issued an urgent call for blood donations and called in off-duty staff to cope with the high number of casualties.
IS threat
Saudi Arabia's large Shia Muslim minority is mainly based in the Eastern Province, and there have been sporadic protests by Shia there for greater rights.The attack on Friday comes at a time when the Saudis are leading a coalition of Arab states in an air campaign against Shia rebels in Yemen.
Saudi Arabia has also been threatened by IS, which is being targeted by a US-led coalition including the Sunni kingdom.
In November last year, an audio recording purported to be from IS chief Abu Bakr al-Baghdadi called on Saudi followers to attack Shia targets.
More than 2,000 Saudis are believed to have joined IS, with hundreds having returned home. Saudi Arabia has launched a security crackdown in recent months, arresting hundreds of IS suspects.