The cross-border raids targeted a group of 60-70 armed members of the outlawed Kurdistan Workers' Party, known as the PKK, said Turkish military officials.
"Our determination to retaliate to attacks that aim against our unity, togetherness and future grows stronger with every action," President Recep Tayyip Erdogan said on Wednesday.
"It must be known that Turkey will not refrain from using its right to self-defence at all times."
Turkish authorities suspect that Wednesday's deadly car bombing in the heart of Ankara targeting military service vehicles was carried out by Salih Necar, a Syrian national who entered Turkey with refugees and had links to Kurdish fighters, it emerged on Thursday.
The attack on Wednesday evening killed 28 people and left 61 wounded, in the latest in a string of deadly strikes in Turkey in recent months.
Police say they have analysed fingerprints from the scene and found a match among the huge database of prints taken from refugees fleeing the five-year war in Syria.
|- Erdogan tells US to choose between Turkey and Kurds
- Who and what are the Kurds fighting for?
- Thousands of Kurds flee Diyarbakir as Turkey expands curfew
- Outrage as Turkish soldiers drag dead Kurd through streets
Reports in both government-leaning and opposition media said Necar was killed in the explosion, without specifying if he had acted as a suicide bomber.
Turkey's air force has been striking PKK positions in northern Iraq since a fragile two-and-a-half-year peace process collapsed in July - shortly after rising support for Kurdish political parties cost President Recip Tayyip Erdogan his desired super-majority in hotly contested parliamentary elections - reigniting a fierce three-decade conflict.
Turkish Deputy Prime Minister Numan Kurtulmus promised on Wednesday that the culprits would be found quickly.
The attack struck the heart of power in the Turkish capital, hitting an area where the headquarters of the army, the parliament and prime minister's offices are in close proximity.
|This attack was carried out by members of the terrorist organisation in cooperation with a YPG member who infiltrated from Syria|
Yeni Safak, the staunchly pro-government daily, reported the attack bore the hallmarks of the Kurdistan Workers' Party (PKK).
But it also said that Necar was himself a member of the Syrian Kurdish Democratic Union Party (PYD), which Turkey accuses of being a "terror group" acting as the Syrian branch of the PKK - a link disputed by Washington.
The head of Syria's PYD on Thursday denied responsibility for the attack.
Turkish Prime Minister Ahmet Davutoglu on Thursday again blamed Kurdish militants in Turkey and Syrian Kurdish fighters for the bombing, saying the bomber was a Syrian national with links to the Kurdish People's Protection Units (YPG), an armed group active in Syria known for making headway in the fight against the Islamic State group and believed to be supported by the Democratic Union Party.
"It has been revealed that this attack was carried out by members of the terrorist organisation in cooperation with a YPG member who infiltrated from Syria," Davutoglu told reporters in Ankara.
A further nine people have been taken into custody over the attack, added the prime minister.
Turkey has for five consecutive days shelled Kurdish areas inside Syria, as YPG fighters advanced upon Syrian-opposition held towns, threatening to cut off Turkish supply lines to rebels.
The PKK, meanwhile, has in recent months killed dozens of soldiers, often in roadside bombings of military vehicles.