Saturday's two explosions hit a lunchtime peace rally in Ankara calling for an end to the renewed conflict between the Kurdistan Workers' Party, or PKK, and Turkish government. Ninety-nine people were killed, Davutoglu said Wednesday, and officials have said more than 240 were injured.
"As the investigation on the attack deepens, through the results on Twitter accounts and IP addresses, we see the high probability that both Daesh (ISIS) and the PKK are organizations that may have had an active role," Davutoglu said, according to the semiofficial Anadolu news agency.
The PKK is a militant group that has fought a long, bitter separatist campaign against the Turkish state for more than 30 years. Hostilities between the two sides resumed after the collapse of a ceasefire in July.
Among those taking part in the targeted peace rally were members of the pro-Kurdish HDP, or Peoples' Democratic Party. The HDP has accused President Recep Tayyip Erdogan and Davutoglu's government of escalating the violence to try to push the party below the 10% electoral threshold to win seats in Turkey's parliament.
The attack came three weeks ahead of a repeat parliamentary election
and at a time when Turkey must deal with the ISIS threat simmering on its southern border.
The Turkish government recently changed its stance to allow the United States to launch strikes on ISIS positions from Incirlik Air Base in southern Turkey. Kurdish forces have been battling ISIS across a swath of northern Iraq and Syria.
Erdogan has said that authorities were conducting DNA tests, checking on intelligence and piecing together evidence to establish who was responsible for the Ankara explosions.
"Important findings had been reached" through the DNA tests, Davutoglu said Wednesday, according to Anadolu. "Detailed investigations continue, especially regarding one assailant. The investigation also continues on other communications links."
A security official who spoke "under customary condition of anonymity" said that two PKK members had been arrested in connection with the blast, the news agency reported.
The official said the two had been linked to a Twitter account that posted "Bomb will explode in Ankara" hours before the blasts, Anadolu said. CNN has not independently verified the report.
Three security officials have been suspended from their positions after the bombings, Turkey's Interior Ministry said in a statement this week. The three included the Ankara police chief, Intelligence Bureau chief and Security Bureau chief, the ministry said.
Attack against Turkey
CNN's Tim Lister writes
that whoever chose to attack the Ankara rally wants to stoke polarization and violence in Turkey -- and destroy an already fragile political dialogue.
On Tuesday, Erdogan insisted that the entire nation had been targeted.
"This attack was against Turkey. The target of this attack was our citizens (in Ankara) as well as the totality of our country," he told reporters.
"All of our institutions are working on this, and the results of this work will show which organizations did this. ... But we must be a little patient. ... I believe we will, together, find out who conducted this heinous act."