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BAGHDAD, Feb 29 (Reuters) - All Turkish troops involved in an offensive against Kurdish rebels inside northern Iraq have withdrawn back into Turkey, Iraqi Foreign Minister Hoshiyar Zebari told Reuters on Friday.

"All the Turkish troops have withdrawn and gone back to the Turkish side of the international border. We welcome this, we think this is the right thing for Turkey to do," Zebari said, adding that the withdrawal took place before dawn on Friday.

A senior Turkish military source said some troops had returned to bases in Turkey after completing their mission against Kurdish PKK rebels, but that no full withdrawal had begun.

A U.S. official in Baghdad also said some troops had left, but that it was too early to call it a withdrawal.

Zebari, who is a Kurd, said Iraq was willing to work with Turkey to resolve the crisis over the presence of the outlawed Kurdistan Workers Party (PKK) in mountainous parts of Iraq's largely autonomous region of Kurdistan.

Turkey sent thousands of troops into the remote region on Feb. 21 to crush PKK rebels who use the area as a base for attacks on Turkish territory.

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