The troops crossed the border as part of a “hot pursuit” of Kurdistan Workers’ Party (PKK) rebels who were involved in a roadside bomb attack that killed 16 soldiers on Sunday, the government official said.
“This is a short-term measure intended to prevent the terrorists’ escape,” the official said.
The private Dogan news agency said two battalions from Turkey’s special forces crossed the border.
A roadside bomb, meanwhile, killed 14 policemen in eastern Turkey after Turkish jets also carried out air strikes against Kurdish rebels and their camps in northern Iraq, according to state media reports.
Kurdish rebels were suspected of detonating a bomb in the eastern province of Igdir as a police vehicle escorting a group of customs officials to a border gate was passing by, the Anadolu Agency reported. Other officers were injured in the attack in the province that borders Armenia, the agency said.
The customs officials were going to a border crossing between Turkey and the Azerbaijani enclave of Nakhchivan following the kidnapping of a group of customs officials by Kurdish rebels. The officials were released unharmed.
The attack on the policemen comes amid a sharp escalation of violence between Turkey’s security forces and the PKK.
The 16 soldiers were killed in a similar attack by PKK on Sunday.
Earlier, Turkey’s state-run news agency said Turkish jets had carried out air strikes against a group of Kurdish rebels as well as the militants’ camps in northern Iraq. It said up to 40 rebels died in the overnight aerial operations.
The air strikes were confirmed by Firat news, a website close to the rebels.
Anadolu Agency said F-16 and F-4 fighter jets bombed a group of up to 25 PKK rebels believed to have carried out the bombing with improvised explosive devices that killed the 16 soldiers near the border with Iraq on Sunday. The agency said the jets struck the rebels on their escape routes in Iraq and also targeted six rebel camps there.
Anadolu said 53 planes were involved in the strikes.
Protests denouncing the PKK erupted in several cities across Turkey on Monday soon after the military announced the 16 soldiers’ deaths. The pro-Kurdish political party said several of its local branches were vandalised during the demonstrations.
More than 200 people have been killed in the renewed fighting between the PKK and the security forces since July, including close to 100 soldiers and police officers.
It comes amid increased political uncertainty in Turkey. The country is holding a new election on November 1 following the ruling party’s failure to form a coalition government after an election in June.
The PKK has been fighting for autonomy in south-eastern Turkey since 1984. It is considered a terrorist group by Turkey and its allies.
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 recriminations between Kurdish groups and Turkey.