ANKARA (Reuters) - Turkey expects Syrian Kurdish fighters to withdraw east of the Euphrates river after they and other U.S.-backed forces seized control of the Syrian town of Manbij from Islamic State last week, Foreign Minister Mevlut Cavusoglu said on Monday.

The Syria Democratic Forces (SDF), a U.S.-backed alliance of Kurdish and Arab fighters, said on Friday they had seized full control of Manbij near the Turkish border in a significant strategic blow to Islamic State.

Turkey views the Kurdish YPG militia as a hostile force, an extension of the outlawed Kurdistan Workers Party (PKK) militant group that has fought a three-decade insurgency in Turkey's southeast, and is considered a terrorist group by the United States and European Union as well as by Ankara.

"Of course we have an expectation," Cavusoglu told reporters in Ankara. "The U.S. promised that the (Syrian Kurdish) forces within the coalition and democratic forces there would move east of the Euphrates again following the Manbij operation."

U.S. Secretary of Defense Ash Carter said in a statement on Monday that liberation of Manbij was an important step in the campaign against the Islamic State, and he thanked the Turkish government for its support.

"For the people of Manbij city, now begins the difficult job of rebuilding their homes and communities, and I call on all of our coalition partners to help them with that task," Carter said.

"For its part, the military coalition will continue to work with capable and motivated local forces to defeat ISIL and ensure it remains defeated," he said, using an acronym for the Islamic State militant group. Carter did not address what would happen with the Syrian Kurdish fighters.

Pentagon spokesman Captain Jeff Davis said the United States has commitments from the Kurdish leadership that the local Arabs liberating their lands will be the ones to rebuild the area.

The operation, in which U.S. special forces played a significant role, marks the most ambitious advance by a group allied to Washington in Syria since the United States launched its military campaign against Islamic State two years ago.

U.S. officials have said that completion of the Manbij operation would create the conditions to move on the militant group's de facto capital of Raqqa.

(Reporting by Gulsen Solaker Addtional reporting by Idrees Ali in Washington; Writing by Daren Butler; Editing by Nick Tattersall, Toni Reinhold)