BEIRUT (Reuters) - The U.S.-backed Syrian Democratic Forces (SDF) said its fighters were waging fierce battles with Islamic State militants in the Old City of Raqqa on Tuesday after the U.S.-led coalition opened two small openings in its historic walls.

The SDF’s media office said four of its fighters were killed in fighting in the Old City. The coalition said on Monday the SDF fighters had breached the Old City after the coalition targeted two 25-meter sections of the 2,500-meter wall.

SDF fighters had seized an ancient palace, Qasr al-Banat, in the eastern part of the Old City, the SDF said in a statement.

An official in the SDF media office said Islamic State had heavily mined the old quarters of Raqqa with devices set off by motion sensor. Islamic State fighters were doing most of their fighting at night and not moving much in the daytime.

The coalition said Islamic State fighters were using the wall as a firing position and had planted “mines and improvised explosive devices at several of the breaks in the wall”, forcing it to open the new breaches in the wall.

“SDF fighters would have been channeled through these locations and were extremely vulnerable as they were targeted with vehicle-borne IEDs (car bombs) and indirect fire as well as direct fire from heavy machineguns, rocket-propelled grenades and snipers as they tried to breach the Old City,” it said.

The SDF launched its assault to capture Raqqa, Islamic State’s de facto capital in Syria, last month after gradually closing in on the city.

The official in the SDF media office, speaking to Reuters by phone, said the Raqqa assault was going to plan though Islamic State tactics including use of the new type of mine and drones that drop bombs had slowed down operations a little.