Turkish forces returned fire on Islamic State militants in Syria with tank shells on Thursday after a Turkish soldier was killed and two others were wounded in a cross-border firefight, the military said.

The fighting comes days after a suspected suicide bombing by the Islamist radical group in a Turkish border town killed 32 people, many of them students and some of them Kurds, touching off waves of violence in the largely Kurdish southeast.

Turkey's NATO allies have long expressed concern about control of the border with Syria, which in parts runs directly parallel with territory controlled by Islamic State. Monday's suicide bombing in the southeastern town of Suruc highlighted fears about the Syrian conflict spilling onto Turkish soil.

The Turkish army has stepped up security along parts of the border, as the conflict in Syria involving Kurdish militia fighters, Islamist militants and Syrian security forces intensifies.

"Turkish soldiers returned fire after shots came from the Syrian side of the border, from the region where Islamic State militants are," a Turkish official said, adding that, in line with the rules of engagement, four tanks returned fire after being fired upon by the militants.

The army said one sergeant had been killed and two others wounded. It said one Islamic State militant had been killed, and that Turkish forces had retrieved his body and rifle.

Another Turkish official said fighter jets had been scrambled to the Syrian border. Turkish jets regularly patrol the 900 kilometre border with Syria.

Rami Abdulrahman, founder of the U.K.-based Syrian Observatory for Human Rights that tracks the conflict in Syria through a network of sources on the ground, gave a different account.

The clashes erupted when two Syrian civilians tried to cross into Turkey and the army opened fire, killing one of them, an elderly man, he said. Islamic State then returned fire and two of their militants were killed, he said.

The Turkish army was not immediately available to comment.

Local media said the fighting was close to the village of Elbeyli, east of Kilis, and an area where the armed forces have sent reinforcements in recent weeks.

Border protection

The skirmish came a day after U.S. President Barack Obama and Turkish President Tayyip Erdogan agreed to work together to stem the flow of foreign fighters and secure the border.

The White House has declined to comment on reports the two had reached a new agreement over the use of the U.S. Air Force's Incirlik base in southern Turkey, from where the U.S. has not been allowed to fly any bombing sorties, but does launch drones.

Ankara has repeatedly said it does not want to mount a unilateral incursion into Syria, but will do what is necessary to protect its border. Around half of the armoured vehicles that patrol Turkey's borders are now along the Syrian frontier.

The clashes were the latest in a wave of violence that followed Monday's suspected Islamic State suicide bombing. Kurdish militants have retaliated by targeting police officers they accuse of collaborating with Islamic State.

One police officer was shot and killed and a second wounded on Thursday in the mainly Kurdish city of Diyarbakir, security sources said.

On Wednesday, two police officers were killed in a town on the Syrian border and militants from the Kurdistan Workers Party (PKK) claimed responsibility.

Turkish police officers stand in front of the coffin of police officer Feyyaz Yumusak, during his funeral procession in southeastern Turkey, Thursday. Yumusak and another officer were found shot dead in their home near Turkey's border with Syria. (Emrah Gurel/Associated Press)

The Suruc bombing enraged Turkey's Kurdish minority, many of whom suspect the government of tacitly backing Islamic State in Syria against Kurdish forces, something Ankara strongly denies.

Turkey has been negotiating an end to the PKK's 30-year campaign for autonomy for Turkey's estimated 14 million Kurds and is worried about its growing influence in war-torn Syria.

Violence has also spread beyond the Kurdish southeast.

In Istanbul, the PKK's youth wing claimed responsibility for the murder of a shopkeeper who the militants said belonged to Islamic State, the Hurriyet newspaper said.

The Turkish military reported a series of attacks by the PKK on Wednesday, though no casualties were reported.

In the eastern province of Tunceli, rebels opened fire on a military base, triggering a brief clash. In Van, near the Iranian border, militants set fire to trucks and opened fire on troops, the military said in a statement.