After breaking an Islamic State group blockade, Syria's army is seeking to encircle the remaining jihadist-held parts of Deir Ezzor city, a military source said Wednesday.

The city is the capital of oil-rich eastern Deir Ezzor province, regarded as a strategic prize by both Russian-backed Syrian troops and US-backed fighters.

In Damascus Wednesday, President Bashar al-Assad said the country was "advancing steadily towards victory thanks to the sacrifices of its army, the determination of its people and the support of its allies," state news agency SANA said.

Last week, Syria's army and allied fighters broke a years-long IS siege of Deir Ezzor, entering two regime-held sections of the city that had been cut off from each other.

Since then, the army has brought reinforcements to the city and is seeking to oust IS from eastern neighbourhoods that run along the Euphrates river, which slices diagonally through the province.

"The army is seeking to encircle Daesh from three sides by controlling the parts of the western bank of the Euphrates river," the source told AFP, using the Arabic acronym for IS.

Troops would target riverside territory on the city's northwestern edges as well as strategic areas on its southern outskirts, including the key military airport and the village of Al-Jafra, on the banks of the Euphrates.

The operation seeks to "oust Daesh from the city and the province completely," the military source said.

Rami Abdel Rahman, head of the Syrian Observatory for Human Rights monitor, also reported that "fierce fighting has been ongoing since yesterday as the army seeks to expel the jihadists and reach the western bank of the Euphrates."

If the army captures Al-Jafra, "Deir Ezzor will be encircled from three sides, so Daesh will have no way out except the Euphrates which is within firing range of regime artillery and Russian warplanes," he added.

As the Syrian army backed by Russian air support battles IS in Deir Ezzor, a separate offensive by the US-backed Syrian Democratic Forces is under way on the eastern side of the province.

The operation by the alliance of Kurdish and Arab fighters began over the weekend, but the SDF has said it was not coordinating the fight with the regime.

Air strikes by Russian and US-led coalition warplanes in support of the separate offensives have killed dozens of civilians in recent days.

On Wednesday, the Observatory said suspected US-led coalition strikes on several parts of eastern Deir Ezzor province overnight and throughout the day killed 12 people.

On Tuesday, the monitor reported 35 people killed in Russian and US-led strikes on either side of the Euphrates.

More than 330,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests.