BBC– Turkish ground forces have crossed into Iraq in pursuit of Kurdish militants for the first time since a ceasefire two years ago.
Government officials said the incursion was a “short-term” measure to hunt down PKK (Kurdistan Workers’ Party) rebels.
Turkish warplanes also launched a wave of air strikes on PKK bases in northern Iraq on Tuesday.
Meanwhile, at least 14 Turkish police officers died in a bomb attack blamed on Kurdish militants on Tuesday.
The attack in eastern Igdir province came a day after suspected PKK bombs killed at least 16 Turkish soldiers in south-eastern Hakkari region.
President Recep Tayyip Erdogan said the PKK had suffered “serious damage” inside and outside of Turkey and was in a state of “panic”.
“Turkish security forces crossed the Iraqi border as part of the hot pursuit of PKK terrorists who were involved in the most recent attacks,” a government source told AFP news agency.
“This is a short-term measure intended to prevent the terrorists’ escape.”
Turkey’s Dogan news agency said two special forces units, supported by warplanes, had attacked two groups of militants.
At least 35 rebels were killed in air raids on bases at Qandil, Basyan, Avashin and Zap early on Tuesday, according to Anadolu news agency.
Spiral of attacks – by Selin Girit, BBC News, Istanbul
Not a day passes by in Turkey these days without violence. And as one attack follows another, emotions are running high.
The funerals of 16 soldiers killed in Sunday’s PKK attack were taking place on Tuesday.
Several thousand people have protested in cities across Turkey against PKK violence and the offices of the pro-Kurdish HDP party have come under attack.
There is now serious concern that the violence could spiral out of control.
Turkey is gearing up for snap elections on 1 November after the ruling AK Party lost its overall majority in June elections and failed to form a coalition government.
It was the HDP that deprived the AKP of its majority, polling over 13% of the vote and entering parliament as a political party for the first time.
Opposition figures have voiced concerns about maintaining election security, especially in Turkey’s predominantly Kurdish east and south-east.
The surge in violence follows the collapse of a ceasefire in July between the army and the PKK.
The truce, which began in 2013, unravelled after a suicide bombing by suspected Islamic State militants near the border with Syria led to mutual recriminations between Kurdish groups and Turkey.
More than 40,000 people have died since the PKK launched its armed campaign in 1984, calling for an independent Kurdish state within Turkey.
In Sunday’s attack, the PKK detonated bombs near two military vehicles in the village of Daglica, close to the border with Iraq.
Prime Minister Ahmet Davutoglu responded by pledging to “wipe out” rebel strongholds.
“Those mountains will be cleared of these terrorists. Whatever it takes, they will be cleared,” he said.
Then on Tuesday, PKK fighters targeted a police minibus as it was heading towards a border post close to the Azerbaijan-run enclave of Nakhchivan, reports said.
Hours later, a policeman was shot dead when suspected PKK militants opened fire on his car in the eastern state of Kunceli.
In a defiant speech in Ankara on Tuesday, Mr Erdogan promised that “with God’s permission, Turkey, which has overcome plenty of crises, will get over the plague of terror”.
Critics accuse President Erdogan of renewing violence to curb support for the pro-Kurdish People’s Democratic Party (HDP), whose 14% share of the vote in June elections cost the governing AKP its parliamentary majority.
The government denies the accusations.