The blasts happened at the Grand Mosque in Kano, the biggest city in the Muslim north of the country, just as Friday prayers had got under way at about 2:00 pm (1300 GMT).
The mosque is attached to the palace of the Emir of Kano Muhammad Sanusi II, Nigeria's second most senior Muslim cleric.
The blasts came after a bomb attack was foiled against a mosque in the northeastern city of Maiduguri on Friday morning, five days after two female suicide bombers killed over 45 people in the city.
"A third one went off in a nearby road close to the Qadiriyya Sufi order. The blasts were followed by gunshots by the police to scare off potential attacks."
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His account was backed up by another witness, Hajara Tukur, who said she lives nearby.
A senior rescue official said 64 bodies had been brought to just one Kano area hospital, while 126 people had been admitted with injuries at three facilities.
"Those figures are going to climb," he told AFP on condition of anonymity, as he was not authorised to speak to the media.
He also cast doubt on Nigerian troops' ability to protect civilians and end the insurgency, in rare public comments by a cleric on political and military affairs.