BEIRUT- The Syrian army and allied forces pushed into the remaining Islamic State-held districts of Deir al-Zor city in eastern Syria on Tuesday, a Hezbollah military media unit said.

Backed by Russian air power and Iran-backed militias, the Syrian army has been fighting in the city since last month, after breaking an Islamic State siege of an enclave there that had lasted three years.

Syrian troops and their allies made gains on Tuesday after "storming districts of Deir al-Zor city to clear them from (Islamic State)", said the media unit run by Lebanon's Hezbollah, a key ally of the Damascus government.

The Syrian Observatory for Human Rights, a Britain-based war monitoring group, said Islamic State militants still controlled nearly five neighbourhoods of the city.

Syrian government forces have been fighting to oust Islamic State from the eastern oil-rich province of Deir al-Zor which borders Iraq. Deir al-Zor city sits on the western bank of the Euphrates river.

In northern parts of the province on the other side of the river, a U.S.-backed alliance of Kurdish and Arab militias is waging their own separate offensive against Islamic State.

Islamic State has lost swathes of territory in Syria and Iraq this year, and in Syria have been pushed into a strip of the Euphrates valley and surrounding desert.

(Reporting by Dahlia Nehme; Editing by Alison Williams) ((dahlia.nehme@thomsonreuters.com))