Anders Behring Breivik, 32, admitted to carrying out both attacks, which he described as "gruesome but necessary".
At least 93 people were killed in the attacks - 96 have been injured and some are still missing.
Memorial services are being held across the country, including at the main Lutheran cathedral in Oslo.
Norway's King Harald V and his wife Queen Sonja attended the cathedral, along with Prime Minister Jens Stoltenberg, laying single white flowers outside as they entered.
The pews in the church were full, with the congregation spilling into the square outside, which was covered in candles and flowers.Mr Stoltenberg told the mourners that the two days since the attacks took place felt like "an eternity - hours, days, and nights filled with shock and angst and crying".
As many of those in the cathedral wept, he said: "Each and every one of those who've left us is a tragedy - together, it's a national tragedy."
On Sunday, police carried out an armed raid on an address in eastern Oslo, detaining several people. They were later released, and police said no explosives were found.
Police said there was no evidence to connect them with the attacks.
In a press conference earlier, police chief Sveinung Sponheim said Mr Breivik "admitted to the facts of both the bombing and the shooting, although he's not admitting criminal guilt".
"He says that he was alone but the police must verify everything that he said. Some of the witness statements from the island have made us unsure of whether there was one or more shooters."
He said police were not looking for anyone else at the moment - though they had not ruled out that the suspect might have had help.
He said Mr Breivik had co-operated during his interrogation and there had been a "good" dialogue. He has been charged over both attacks, and is due to appear in court on Monday.
Mr Sponheim confirmed that the maximum time Mr Breivik could face in prison under Norwegian law is 21 years.
At least seven people were killed on Friday in a bomb attack on the government quarter in Oslo. Soon afterwards, 85 people were shot dead as a gunman, dressed as a policeman, ran amok on the nearby island of Utoeya. An 86th person died in hospital on Sunday.
The gunman was arrested when police arrived an estimated 90 minutes after the massacre began. Mr Breivik's lawyer said his client surrendered after running out of ammunition.
At least four people from the island camp shooting are yet to be found; it is thought some may have drowned after swimming out into the lake to escape the hail of bullets.
Police are using a mini-submarine to search for the missing bodies.
In Oslo police said the death toll could rise further as bodies or body parts were in buildings damaged by the bomb but still too unstable to search.
Years of planning
"He thought it was gruesome having to commit these acts, but in his head they were necessary," Mr Breivik's lawyer Geir Lippestad told Norwegian media.
"He wanted a change in society and, from his perspective, he needed to force through a revolution," Mr Lippestad said. "He wished to attack society and the structure of society."
He added that the actions had been planned for some time.
The suspect is reported to have had links with right-wing extremists.
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.
A 1,500-page document written in English and said to be by Mr Breivik - posted under the pseudonym of Andrew Berwick - was also put online hours before the attacks, suggesting they had been years in the planning.
The document and the video repeatedly refer to multiculturalism and Muslim immigration; the author claims to be a follower of the Knights Templar - a medieval Christian organisation involved in the Crusades, and sometimes revered by white supremacists.
Police have not speculated on motives for the attack but the bomb in Oslo targeted buildings connected to Norway's governing Labour Party, and the youth camp on Utoeya island was also run by the party.
In the document posted online, references were made to targeting "cultural Marxists/ multiculturalist traitors".His lawyer, Mr Lippestad, said: "He's stated that he went to Utoeya to give the Labour Party a warning that 'doomsday would be imminent' unless the party changed its policies."
Mr Lippestad says the suspect remained calmed and balanced throughout a 10-hour night of interrogation.
"I think he's realised what he's done, and he views himself as sane," he said.
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, says the BBC's Richard Galpin, near the island which remains cordoned off by police.
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