AMMAN (Reuters) - U.S. backed Syrian forces fought their way to the western entrance of Manbij city for the first time since a major offensive to seize the last territory held by ultra-hardline militants on the Syria-Turkey border, a source in the Syrian group said on Saturday.

The source from the Syria Democratic Forces (SDF) alliance, which includes the powerful Kurdish YPG militia and Arab fighters, told Reuters their troops were now almost two kilometers from the city center.

Since the start of the offensive on May 31, the SDF has taken dozens of villages and farms around Manbij but had held back from entering the city with many thousands of people still trapped there.

(Reporting by Rodi Said near Manbij; Writing by Suleiman Al-Khalidi; Editing by Jon Boyle)