DAMUSCUS, Dec. 13 (CGTN) -- Up to 15,000 Syrian rebels are ready to join a Turkish military offensive against U.S.-backed Kurdish forces in northeast Syria, but no date has been set for the operation, a spokesman for the main Turkish-backed Syrian rebel group said on Thursday.

President Tayyip Erdogan said on Wednesday that Turkey would launch the offensive in a few days, targeting a border region east of the Euphrates river which is held by the YPG (Kurdish People's Protection Units) Kurdish militia.

The announcement prompted a sharp rebuke from the Pentagon, which said any unilateral military action into northeast Syria would be unacceptable.

The United States has been supporting the YPG in the fight against Islamic State insurgents since 2015. Following cross-border shelling from Turkey into Kurdish-controlled territory two months ago, U.S. forces have set up three military observation posts near the border.

Turkey says the YPG is a terrorist organization and an extension of the outlawed Kurdistan Workers Party (PKK), which has waged an insurgency against the state in southeastern Turkey for more than three decades.

On Thursday the Turkish military said one of its soldiers stationed in Syria's Afrin region was killed by fire from YPG fighters, who were in the Tel Rifaat area. Both areas are west of the Euphrates in northern Syria.

Turkish forces returned fire, the military said.

Turkey has already swept YPG fighters from Afrin and other areas west of the Euphrates in military campaigns over the past two years, but has not gone east of the river – partly to avoid direct confrontation with U.S. forces.

The spokesman for the National Army, a Turkish-backed rebel force aimed at unifying disparate factions in northwest Syria, said on Thursday that there was no set date for the operation, which would start from both Syrian and Turkish territory.

“The battle will be launched simultaneously from several fronts,” Major Youssef Hamoud said, adding that the operation from Turkey might begin a few days before the move from within Syria.

In a speech on Wednesday, Erdogan said that Turkey's target “is never U.S. soldiers”.

Commander Sean Robertson, a Pentagon spokesman, said in a statement that unilateral military action into northeast Syria by any party would be of grave concern, “particularly as U.S. personnel may be present or in the vicinity.”