No group has said it carried out the attack, but the government believes that two male suicide bombers caused the explosions, hitting a peace rally.
The official death toll is 97, but one of the main groups at the march put the number of dead at 128.
The funerals of more of the victims are taking place on Monday.
Saturday's twin explosions ripped through a crowd of activists gathering outside the main railway station in the Turkish capital.
They were due to take part in a rally calling for an end to the violence between Turkish government forces and the militant Kurdistan Workers' Party (PKK).
There is anger in Turkey that authorities were unable to prevent such a major attack in the heart of the capital city - and some scepticism from opposition groups about the government's claims.
Mr Davutoglu said authorities were close to identifying one of the suicide bombers, and that this would help to pinpoint which group carried out the attack.
He had previously said that IS, the PKK and far-left groups were all capable of such an attack.
Some local media have implicated the brother of a man who carried out an IS bombing in the southern border town of Suruc in July, which killed more than 30 people.
There are also reports that investigators believe there are similarities between the device used in that attack and those used on Saturday.
Turkey announced after the Suruc bombing that it would allow its southern Incerlik airbase to be used by the US-led coalition targeting IS in Syria. Turkey, a Nato member, shares a long land border with its unstable southern neighbour.
The Ankara bombings are the most deadly in Turkey's history. The German chancellor, Angela Merkel, is due to visit the country on Tuesday.
"These attacks will not turn Turkey into a Syria," Turkish Prime Minister Ahmet Davutoglu said on Monday.
Speaking on Turkish television, Mr Davutoglu said the bombings were an attempt to influence the forthcoming elections, due to take place on 1 November after a vote in June left no party able to form a government.
Many of the victims were activists of the pro-Kurdish HDP party, which says it is now considering cancelling all election rallies.
The HDP believes its delegation at the march was specifically targeted.
The party gained parliamentary seats for the first time in June's vote, depriving President Recep Tayyip Erdogan's governing AK Party of its majority.
The situation in Turkey was tense even before the Ankara bombings: the ceasefire with the PKK had broken down and there had been clashes between the militants and security forces, killing at least 150 since July.
On Saturday the PKK unilaterally declared a new ceasefire. However, this was rejected by the Turkish government, which carried out cross-border air strikes on PKK positions in southern Turkey and Iraq on Sunday.
The BBC's Mark Lowen in Ankara says that critics of the Turkish government believe it is using IS as a scapegoat - and that murky elements of a so-called "deep state" are to blame for the bombings, aiming to shore up support ahead of the elections.
The leader of the HDP, Selahattin Demirtas, said the state had attacked the people - and that the people of Turkey should be the recipients of international condolences, not President Erdogan.
Thousands of people attended the funeral of victim Uygar Cosgun on Monday, some of them chanting anti-government slogans, said the BBC's Middle East editor Jeremy Bowen.
One of the victims of Saturday's attacks has been identified as 70-year-old Meryem Bulut, a member of the Saturday Mothers group, who have protested about their missing sons since the 1990s.