245 others are injured.
The attack apparently targeted a peace rally to denounce the increased violence between Kurdish rebels and Turkish security forces.
Hours after the attacks, the Turkish government imposed a temporary news blackout covering images that showed the moment of the blasts, gruesome or bloody pictures or "images that create a feeling of panic". A spokesman warned media organisations they could face a "full blackout" if they did not comply.
Many people in Ankara reported being unable to access Twitter and other social media websites after the blasts. It was not clear if authorities had blocked access to the websites, but Turkey often does impose blackouts following attacks.
The attack comes weeks before Turkey's November 1 elections.
Prime Minister Ahmet Davutoglu called an emergency security meeting to discuss the attack. His office said he was suspending his election campaign programmes for the next three days. President Recep Tayyip Erdogan cut short his programme in Istanbul to return to the capital.
"There was a massacre in the middle of Ankara," said Lami Ozgen, head of the Confederation of Public Sector Trade Unions, or KESK. "Two bombs exploded in very short intervals."
"The toll is severe," said Selahattin Demirtas, leader of Turkey's pro-Kurdish party, whose members attended the rally. "There are dozens of dead and hundreds of injuries. Some of our friends are in serious condition."
In July, a suicide bombing blamed on the Islamic State group killed 33 people in a town near Turkey's border with Syria.
