The car bomb detonated when a convoy of military buses carrying dozens of soldiers stopped at traffic lights in central Ankara, sparking panic and chaos.
"This attack has very clearly targeted our esteemed nation as a whole and was carried out in a vile, dishonourable, treacherous and insidious way," said Kurtulmus.
Plumes of smoke could be seen from all over the city rising from the scene, close to the headquarters of the Turkish military and the parliament.
The powerful blast was heard throughout Ankara, sending alarmed residents rushing to their balconies.
"I saw a huge fireball growing," 25-year-old witness Gurkan, who said he was standing 500 metres (yards) from the scene, told AFP.
"People started to run in all directions in panic as soon as we heard a strong explosion."
The army said the attack took place at 1631 GMT and had targeted "service vehicles carrying army personnel".
- 'Right to self defence' -
Without specifying what the retaliation could entail, Erdogan warned that "Turkey will not shy away from using its right to self-defence at any time, any place or any occasion".
The bombing prompted Prime Minister Ahmet Davutoglu to scrap a planned trip to Brussels on Thursday to discuss Europe's migrant crisis. Erdogan also shelved a trip to Azerbaijan.
In Ankara, ambulances and fire engines were sent to the scene and wounded victims were seen being taken away on stretchers.
Images showed firefighters trying to overcome a fierce blaze engulfing the gutted service buses.
Turkish police threw a security cordon around the area. A second blast later rocked the area, an AFP correspondent said, but officials said this was police detonating a suspicious package.
Washington in a statement strongly condemned "the terrorist attack on Turkish military personnel and civilians" and reaffirmed US solidarity with the key NATO partner.
NATO Secretary General Jens Stoltenberg said the alliance strongly condemned the bombing. "NATO Allies stand shoulder to shoulder in the fight against terrorism," he said.
The EU pledged to stand "with Turkey and its people in these difficult times".
- 'Perpetrators will be revealed' -
Kurtulmus said authorities did not know who had carried out the attack, but vowed the perpetrators "will be revealed as soon as possible".
Ankara was already on alert after 103 people were killed on October 10 when two suicide bombers blew themselves up in a crowd of peace activists, the bloodiest attack in the country's modern history.
Eleven people, all German tourists, were also killed on January 16 when a suicide bomber blew himself up in the tourist heart of Turkey's biggest city Istanbul.
Those attacks were blamed on Islamic State jihadists, as were two other deadly bombings in the country's Kurdish-dominated southeast earlier in the year.
But Turkey is also waging an all-out assault on the outlawed Kurdistan Workers' Party (PKK), which has repeatedly attacked members of the security forces with roadside bombings on their convoys in the southeast.
The PKK launched an insurgency against the Turkish state in 1984, initially fighting for Kurdish independence although now more for greater autonomy and rights for the country's largest ethnic minority.
Turkish artillery in the south of the country shelled positions of Kurdish fighters in Syria for the fifth day in a row on Wednesday in an escalating standoff, reports said.
Turkey says the Syrian Kurdish Democratic Union Party (PYD) and its People's Protection Units (YPG) are merely the Syrian branch of the PKK and themselves terror groups.
The banned ultra-left Revolutionary People's Liberation Party–Front (DHKP-C) has also staged a string of usually small-scale attacks in Istanbul over the last few months.