Goodluck Jonathan urged the nation “to confront the common enemy” after the gun and bomb attack during Friday’s prayers in the northern city of Kano.
Hundreds of people were injured in an attack which officials say bears the hallmarks of Boko Haram militant group.
No-one has so far said that they carried out Friday’s assault.
Kano’s Central Mosque, where the attack took place, is where the influential Muslim leader, the emir of Kano, usually leads prayers.
He recently called for people to arm themselves against Boko Haram, so it is possible that this attack was in response to that call, says the BBC’s Will Ross in Abuja.
Boko Haram, a Sunni Islamist group, has been waging an insurgency in Nigeria since 2009 and has killed more than 2,000 people this year, human rights groups say.
President Jonathan ordered the country’s security services “to launch a full-scale investigation and to leave no stone unturned until all agents of terror undermining the right of every citizen to life and dignity are tracked down and brought to justice”.
He said Nigerians should “remain united to confront the common enemy”.
The government, he said, would “continue to take every step to put an end to the reprehensible acts of all groups and persons involved in acts of terrorism”.
Reuters news agency counted 81 bodies in two separate mortuaries following the attack on the Central Mosque.
An AFP reporter at counted 92 bodies at the Murtala Mohammed Specialist Hospital mortuary alone. Most victims were men or boys with blast injuries and severe burns.
As BBC’s Tomi Oladipo reports, the gunmen opened fire on people as they tried to escape
Three bomb explosions were reported in and around the mosque. The attackers also shot at worshippers.
Some reports say the first bomb was hidden in a car which was driven straight into the worshippers.
One eyewitness told the BBC’s Focus on Africa: “The imam was about to start prayer when he saw somebody in a car trying to force himself into the mosque. But when people stopped him, he detonated the explosions. People started running helter-skelter.”
Several men then opened fire on the crowd, killing more people. Three of the gunmen were caught and killed on the spot, the BBC’s Will Ross reports.
BBC Hausa editor Mansur Liman said one witness at a local hospital had described the scenes there as being the most horrible he had ever seen.
Boko Haram has stepped up attacks against civilian targets since the Nigerian military launched an offensive last year.
The group carries out almost daily attacks mostly in the north-east of the country. Also on Friday, the security forces said they had foiled an attempt to attack worshippers in the north-eastern city of Maiduguri, defusing six bombs planted in a mosque and a nearby market.
The militants were also behind the kidnapping of more than 200 schoolgirls from Chibok in Borno state this year, an act that sparked international outrage.