A 32-year-old Norwegian man was charged over both attacks, but police say it is possible another person was involved.
The suspect's lawyer said he admitted responsibility for the attacks.
He said his client believed his actions were "atrocious" but "necessary", adding that he would explain himself in court on Monday.
The suspect surrendered when approached by police officers, police said.
End Quote Adrian Pracon SurvivorPeople were falling dead right in front of me”
However, the buildings were currently too fragile and dangerous to search, and there were still undetonated explosives there, the police chief said.
It was possible the total death toll from the two attacks could rise to 98, he said.
Prime Minister Jens Stoltenberg comforted victims and relatives alongside King Harald, Queen Sonja and Crown Prince Haakon in the town of Sundvollen near the island.
Mr Stoltenberg said he was "deeply touched" by the meetings.
"We will do whatever we can to give them as much support as possible," he said.
At the sceneThousands of people have come to the perimeter of the government quarter in downtown Oslo where the bomb went off on Friday. They have come to have a look at the destruction, lay flowers and many are just standing in silence. Churches across the city and the entire country have opened their doors and many are packed.
The area is still cordoned off and the army is manning many checkpoints - a sight never seen before in this normally peaceful city.
The downtown square which is overlooked by the now ruined building housing the PM's office would normally be crowded with people enjoying a drink and the sunshine - instead it is blocked off and the only people here are soldiers, police and those clearing the broken glass and rubble. It will be some time before this city gets back to some sort of normality.
He has been named as Anders Behring Breivik. Police searched his Oslo apartment overnight and are questioning him.
Still pictures of him, wearing a wetsuit and carrying an automatic weapon, appeared in a 12-minute anti-Muslim video called Knights Templar 2083, which appeared briefly on YouTube.
The BBC's Richard Galpin, near the island which is currently cordoned off by police, says that Norway has had problems with neo-Nazi groups in the past but the assumption was that such groups had been largely eliminated and did not pose a significant threat.
Meanwhile a farm supply firm has confirmed selling six tonnes of fertiliser to Mr Breivik, who is reported to have run a farming company. Speculation has been rife that fertiliser could have been used in the Oslo bomb.
The number killed in the island shooting spree, which is among the world's most deadly, had been put at 10 on Friday - but soared overnight. Hundreds of young people had been attending the summer camp organised by the governing Labour Party on Utoeya island.
Eyewitnesses described how a tall, blond man dressed as a policeman opened fire indiscriminately, prompting camp attendees to jump into the water to try to escape the hail of bullets.
Island shooting suspect
- Describes himself as a Christian and conservative on Facebook page attributed to him
- Grew up in Oslo and attended Oslo School of Management
- Set up farm through which he would have had access to fertiliser - which can also be used to make a bomb
Police say they discovered many more victims after searching the area around the island. They have warned the death toll may rise further as rescue teams continue to scour the waters.
The gunman is reported to have been armed with two weapons, one of them an automatic rifle.
NRK journalist Ole Torp told the BBC the suspect went to the island dressed in a police uniform, asked people to gather round and then started shooting.
The attacks sparked strong international condemnation, with US President Barack Obama expressing his condolences and offering support.
Britain's Queen Elizabeth spoke of her shock and sadness in a letter to King Harald.
The BBC's John Sopel in Oslo says the city is strangely quiet and there is a heavy military presence, with checkpoints around the government quarter.
Officials have urged people to stay at home and avoid central areas of the city.