By Suleiman Al-Khalidi

AMMAN (Reuters) - Islamic State militants on Saturday pushed back U.S.-backed forces trying to advance into their stronghold of Manbij for the first time since a major offensive to capture the city and cut off the militants' main strategic access route to Turkey, a monitoring group and Kurdish sources said.

The Syria Democratic Forces (SDF), comprised of Kurdish and Arab fighters and backed by the air power of a U.S.-led coalition to fight Islamic State and aided by U.S. special forces, have been involved in the month-long Manbij operation aimed to seal off their last stretch of Syrian-Turkish frontier.

The British-based Syrian Observatory for Human Rights confirmed the militants had evicted SDF troops from a main district south of the city which has been the scene of heavy fighting after suicide bombers blew up an explosive-laden car.

The militants also recaptured a village northwest of the city.

An SDF spokesman, however, denied reports they had pulled back from positions inside the city and said the campaign to uproot the militants would continue until they "liberated Manbij".

"I stress that we have not retreated any step and all our positions are under our control," Sharfan Darwish, spokesman for the SDF-allied Manbij Military Council, said in a statement.

The U.S.-backed forces have been bogged down in fighting in the northern and southern outskirts of the city after rapid advances that began with the capture of dozens of villages around the city until they surrounded it from all sides.

Progress in storming the city has been slow with the militants using snipers, planting mines and preventing civilians from leaving, hampering U.S. airpower's ability to bomb the city without causing large casualties, Kurdish sources said.

Fighting was mainly focused near a major grain silo complex south of the city that had been hit by U.S.-led coalition jets.

Manbij's loss would be a big blow to the militants as it is of strategic importance, serving as a conduit for transit of foreign jihadists and provisions coming from the Turkish border.

Brett McGurk, U.S. President Barack Obama's special envoy in the fight against Islamic State, said on Tuesday once the operation in northern Syria is completed, it would create the conditions to move on the militant group's de facto capital of Raqqa. U.S. officials have anticipated a tough battle ahead.

The Manbij operation 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.

(Reporting by Suleiman Al-Khalidi and Rodi Said in Kobani Syria; Editing by Marguerita Choy and James Dalgleish)