By Orhan Coskun

ANKARA (Reuters) - Turkish forces returned fire on Islamic State fighters in Syria with artillery and tank shells on Thursday after a Turkish soldier was killed and two others wounded in a cross-border firefight.

The fighting comes days after a suspected suicide bombing by the Islamist radical group killed 32 people, some of them Kurds and many of them students, in a Turkish border town, 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 in a statement on its website that one sergeant had been killed and two others wounded, while one Islamic State militant had been killed.

Another official said fighter jets had been scrambled to the Syrian border. Turkish jets regularly patrol the 900 km (560 mile) border with Syria.

The clashes took place just east of Kilis in a border area where Islamic State transports equipment and fighters into Syria, said Rami Abdulrahman, founder of the London-based Syrian Observatory for Human Rights, citing sources on the ground.

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

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.

Around half of the armored vehicles which patrol Turkey's borders are now along the Syrian frontier, Reuters reported earlier.

Turkey has repeatedly said it does not want to mount a unilateral incursion into Syria, but will do what is necessary to protect its border.

Southeastern Turkey has been hit by waves of violence since Monday, when a suspected Islamic State suicide bomber killed 32 mostly young students in a border town.

Kurdish militants have targeted police officers whom they accuse of collaborating with Islamic State.

(Additional reporting by Seymus Cakan in Diyarbakir; Ayla Jean Yackley in Istanbul and Ece Toksabay; Writing by David Dolan; Editing by Nick Tattersall and Ralph Boulton)