BEIRUT (Reuters) -- The Syrian Kurdish YPG militia said it began an advance towards an Islamic State-held town at the Turkish border on Saturday, thrusting deeper into the jihadists' stronghold of Raqqa province in a campaign backed by U.S.-led air strikes.

Redur Xelil, the YPG spokesman, told Reuters the YPG and smaller Syrian Arab rebel groups fighting alongside it had begun the move towards Tel Abyad after encircling the Islamic State-held town of Suluk 20 km (12 miles) to the southeast.

The advance raises the prospect of a battle at the Turkish border between the well-organized YPG militia and Islamic State. Tel Abyad is important to Islamic State as the nearest border town to its de facto capital of Raqqa city.

Fighting near the border has already forced more than 13,000 people to cross into Turkey from Syria. Some 1,500 more are waiting to cross. Turkish soldiers sprayed water and fired into the air when some of them approached the border fence on Saturday, a security source said.

The YPG has made a determined push into Raqqa province from neighboring Hasaka where, with the help of the U.S.-led alliance, it has driven Islamic State from wide areas of territory since early May.

"The move towards Tel Abyad from the east began today after the completion of the Suluk blockade," Xelil said. "Many of the Daesh militants have fled (Suluk), apart from a group of suicide attackers inside the town and the booby traps, so we are very cautious about entering the town center," he added via Skype.

Daesh is an Arabic name for Islamic State.

The Syrian Observatory for Human Rights, a UK-based organization that tracks the war, said the YPG fighters were now half-way between Suluk and Tel Abyad, situated across the border from the Turkish town of Akcakle.

Turkey's Worries

For the YPG, seizing Tel Abyad would help them link up Kurdish-controlled areas in Hasaka province and Kobani.

The expansion of Kurdish influence in Syria near the border with Turkey is a concern for Ankara, which has long been worried about separatism among its own Kurdish population.

The Turkish authorities have closed Akcakale to vehicles and it has been months since they allowed anyone to cross from Tel Abyad into Turkey. However, Turkey still allows people with a valid passport to cross into Syria from Akcakle.

The Turkish military has dug trenches in the border area.

With the help of U.S.-led air strikes, the YPG fended off an Islamic State attack on the border town of Kobani, or Ayn al-Arab, in January. Since then, the YPG has emerged as the most significant partner on the ground in Syria for the U.S.-led alliance that is trying to roll back Islamic State.

Washington has ruled out the idea of partnering with President Bashar Assad, who last month lost the city of Palmyra in central Syria to Islamic State -- the first time the jihadists seized a city directly from government control.

Turkish President Tayyip Erdogan on Thursday accused the West of bombing Arabs and Turkmens in Syria while supporting Kurdish "terrorist" groups he said were filling the void left behind.

Xelil said: "The help of the alliance forces has been very effective and accurate in its target selection."

The YPG is affiliated to the outlawed Kurdistan Workers Party (PKK) which has fought a decades-long insurgency against the Turkish state. The PKK is considered a terrorist group by Ankara, the United States and European Union.