Another 16 soldiers were wounded in the attack in the Daglica area of Hakkari province, which borders northern Iraq's Kurdish areas, the governor's office in Hakkari said.
Prime Minister Recep Tayyip Erdogan, speaking to reporters in Mexico where he is attending a Group of 20 summit, said his government was determined to press ahead with the fight against the PKK "until the end" and repeated a call on the group to lay down arms.
"Sooner or later, we will succeed," Erdogan said in televised remarks. "There is just one thing the terrorists must do and that it is to lay down arms."
The military's top brass rushed to the area to assess the situation as the Cabinet convened to discuss the attack.
A statement released after the meeting said unmanned drones, fighter jets and helicopters were sent to back up troops deployed to fight the rebels. The rebel death toll, initially announced as 10, increased to 18 by the late afternoon.
The rebel group, the Kurdistan Workers' Party, or PKK, is fighting for autonomy in southeast Turkey. Tens of thousands have died since it took up arms in 1984.
A similar rebel attack in the same area in late 2007, when 12 Turkish soldiers died, triggered an eight-day incursion by the Turkish military into Iraq in February 2008. Rebels use northern Iraq as a base to launch attacks on Turkish troops.
An estimated 20 percent of Turkey's 75 million people are Kurds. Tuesday's attack came amid efforts by the government to try to reconcile with the Kurdish minority by granting more cultural rights.
Erdogan recently announced plans to introduce elective Kurdish lessons in schools, after allowing Kurdish language broadcasts on television, Kurdish-language institutes and private Kurdish courses. Turkey refuses demands by Kurdish activists and politicians to hold full education in Kurdish, fearing that it could divide the country along ethnic lines.
Faruk Bal, deputy chairman of a nationalist opposition party, told TRT television Tuesday that his party will not join the search for a political solution to the conflict because it is against giving any concessions to the rebel group, which is considered a terrorist organization by the United States and the European Union.
"Today's violence shows that whatever you give, they will ask for more as long as they have their weapons in their hands," Bal said.
The 27-nation EU, which Turkey is striving to join, has pushed the Turkish government to grant more rights to the Kurds. But EU countries also have urged Kurdish lawmakers to distance themselves from the PKK.
"The PKK should cease every kind of armed action," Selahattin Demirtas, chairman of the pro-Kurdish Peace and Democracy Party, told a meeting of Kurdish lawmakers in Parliament after the attack. "The government should also end military operations."
A senior Kurdish rebel commander, Bahoz Erdal, ruled out a cease-fire or laying down arms in remarks published Tuesday by the pro-Kurdish Firat news agency.