BEIRUT (Reuters) - Syrian militias backed by U.S.-led air strikes have repelled a second Islamic State counter attack in 24 hours near a city being targeted in a major offensive against the jihadist group, an official and a monitoring group said on Monday.

The Syria Democratic Forces (SDF) alliance grouping Kurdish and Arab fighters launched an offensive last month to capture the city of Manbij from Islamic State, part of an operation aimed at dislodging the group from the border with Turkey.

Islamic State, seeking to break a siege on Manbij, counter attacked on three fronts around the city on Saturday, followed by a further counter attack over Sunday night and in the early hours of Monday, the Syrian Observatory for Human Rights and an SDF official said. Both assaults had been repelled, they said.

"Dozens of air strikes repelled (Islamic State forces)," Rami Abdulrahman, director of the Britain-based Syrian Observatory for Human Rights, said.

"The SDF has made no progress in Manbij for 10 days," he said, noting that progress had been slow in part because Islamic State fighters had heavily mined buildings in the city.

The U.S.-backed campaign in northern Syria aims to drive Islamic State away from its last foothold at the border with Turkey. Syrian government forces, backed by Russia, are waging a separate campaign against the jihadists in the same area.

The United States has ruled out cooperating with Damascus in the war against Islamic State.

(Writing by Tom Perry; Editing by Louise Ireland)