Turkish demonstrators protest an attack by Kurdish rebels that killed 28 soldiers in southeast Turkey on Wednesday, marking one of the deadliest days for the army in the 27-year battle against the separatists. (Ade Maltan/AFP/Getty Images)

Turkish military aircraft entered Iraqi airspace Wednesday morning in “hot pursuit” of Kurdish rebels who hours earlier had killed 28 soldiers along the turbulent border, according to Prime Minister Recep Tayyip Erdogan.

“We will never bow to any attack from inside or outside Turkey,” Erdogan said in a televised news conference.

The rebels, part of the Kurdistan Workers Party (PKK) that is fighting for autonomy in Turkey, attacked military outposts and police stations near the Turkish border towns of Cukurca and Yuksekova, according to several press reports. The Turkish retaliation, which drew support from the United States and NATO, began soon afterward, with air force bombers and helicopter gunships leading the charge.

At least 20 Kurdish rebels were killed in the counteroffensive, the Istanbul-based Dogan news agency reported, although PKK leader Duzdan Hammo maintained that there were no rebel casualties as of Wednesday evening and that the number of Turkish fatalities was higher than reported.

“Turkish forces have provoked our fighters to conduct attacks,” Hammo said in a phone interview. “There is still a lot of heavy shelling on the border.”

Jabbar Yawar, secretary general of Kurdistan’s Peshmerga Armed Forces, disputed reports Wednesday afternoon that Turkish soldiers had entered Iraq on foot. Turkish air raids were conducted overnight and into the morning, said Col. Hussein Tamir, border brigade commander of Kurdistan’s Dahuk province.

The government of the semiautonomous Iraqi Kurdistan region called the PKK assault “a crime” that was “against the interests of the Kurdish people.”

“We call for an immediate cease-fire,” said the office of Kurdistan President Massoud Barzani in a written statement. “Problems will never be solved by war.”

Iraqi Prime Minister Nouri al-Maliki’s office did not respond to calls for comment on clashes that continue to roil the winding border between southeastern Turkey and Iraq’s northern provinces.

More than 40,000 people have been killed in the border conflict since 1984, when the PKK launched a violent and prolonged campaign for independence in Turkey. The United States has designated the PKK a terrorist group.

“The United States strongly condemns this morning’s outrageous terrorist attack against Turkey, one of our closest and strongest allies,” President Obama said in a written statement Wednesday. “I offer my condolences to the families of the victims and to all of the Turkish people.”

Turkey has previously asked the Obama administration to base a fleet of U.S. Predator drones on Turkish soil for counterterrorism operations in northern Iraq, a region rife with conflicts between Turkmen, Kurds, Arabs and Iranians. Turkish airstrikes have killed more than 150 Kurdish militants since mid-August in retaliation for PKK attacks, according to the Turkish military. A small number of civilians in northern Iraq have been killed and hundreds have been displaced by the conflict, Human Rights Watch has reported.