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Iraqi special forces reached the eastern bank of the Tigris river in Mosul on Sunday for the first time in a U.S.-backed assault on ISIS, military officials said.

Elite counter-terrorism service (CTS) units fought their way to a bridge over the Tigris which has been damaged in fighting, CTS spokesman Sabah al-Numan said.

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It was the first time Iraqi forces have reached the river in the city itself since the operation to drive IS out of Mosul began in October. Iraqi forces have so far only penetrated eastern districts of Mosul, which is bissected by the river. The city is Islamic State's last major stronghold in Iraq.

CTS forces backed by U.S.-led air raids meanwhile clashed with Islamic State militants near a historic site a short distance away, an officer said, as they tried to drive the jihadists out of more districts in the city.

An Iraqi man carries his children near the town of Bartella as people return to their liberated neighbourhoods in eastern Mosul, Saturday. DIMITAR DILKOFF / AFP - Getty Images

"This morning CTS troops advanced in two directions towards the Baladiyat and Sukkar districts," Lt.General Abdelwahab al-Saadi said.

"During the advance, Daesh [ISIS] tried to confront us from the historic hill," he said, apparently referring to a hill located near the ruins of the ancient Assyrian city of Nineveh, east of the Tigris river and inside Mosul.

Saadi said Iraqi forces and warplanes from the U.S.-led coalition "dealt with" IS fighters who had gone up the hill to use it as a firing position. Dozens of the militants were killed, he added.

The CTS has spearheaded advances into eastern Mosul in the nearly 12-week campaign.

Forces including the CTS and army units have advanced further into Mosul in recent days, helped by new tactics and better coordination to gain fresh momentum after getting bogged down inside the city towards the end of the year.