Mr Erdogan said the suicide car bomb would serve only to strengthen the resolve of Turkey's security forces.
At least one suspected bomber, who sources say was a female member of the Kurdish rebel PKK, also died.
Turkish planes bombed PKK targets in Iraq. Officials suspect the group is behind the attack.
Eleven warplanes carried out air strikes on 18 targets including ammunition dumps and shelters in the Qandil and Gara sectors, the army said. The PKK [the outlawed Kurdistan Workers Party] confirmed the attacks.
How dangerous is Turkey's unrest?
Tears and destruction amid PKK crackdown
Meanwhile curfews have been imposed in two mainly Kurdish towns in south-eastern Turkey, Yuksekova and Nusaybin, as security operations are carried out against Kurdish militants, Anadolu news agency reports.
Another curfew is due to start in the city of Sirnak at 23:00 local time (21:00 GMT).
No group has admitted carrying out the Ankara attack, but government sources had cast suspicion on the PKK.
Interior Minister Efkan Ala said an investigation would conclude on Monday and those responsible would be named.
Unnamed officials said the female bomber was a member of the PKK from the eastern town of Kars who joined the group in 2013.
Kurdish rebels have carried out a series of attacks on Turkish soil in recent months, and security forces have raided Kurdish areas, after a ceasefire ended last year. The so-called Islamic State group has also targeted Ankara recently.

But the BBC Turkish service's Enis Senerdem says that Ankara is the powerhouse of government and the attack sends a clear message that the establishment is under fire.
Mr Erdogan's call for people to remain calm has not resonated, he adds.
Turkey's pro-Kurdish political party issued a statement condemning the attack. The Peoples' Democratic Party (HDP) said it shares "the huge pain felt along with our citizens".
The HDP is frequently accused of being the political wing of the PKK, an accusation it denies, and of not speaking out against PKK violence.
Last month, a bomb attack on a military convoy in Ankara killed 28 people and wounded dozens more.
That bombing was claimed by a Kurdish militant group, the Kurdistan Freedom Hawks (TAK). It said on its website that the attack was in retaliation for the policies of President Erdogan.
Turkey, however, blamed a Syrian national who was a member of the YPG.
Last October, more than 100 people were killed in a double-suicide bombing at a Kurdish peace rally in Ankara.