Turkey's military says fighter jets have bombed suspected Kurdish rebel targets in a new cross-border offensive in northern Iraq.

A military statement on Saturday said the overnight airstrikes hit suspected Kurdistan Workers' Party, or PKK, hideouts, shelters and supply points in four areas of northern Iraq. Areas targeted included the Qandil mountains where the PKK's leadership is based.

Separate raids were also conducted on PKK caves, shelters and weapon emplacements in Turkey's mainly Kurdish Sirnak province, the military said.

Turkey has been striking PKK targets in northern Iraq and southeast Turkey since July, when violence between the rebels and Turkey's security forces re-ignited, killing hundreds of people and derailing a fragile peace process.