BEIRUT (Reuters) - U.S.-backed Syrian militias will not let government forces cross the Euphrates River in their bid to recover eastern Syria, their commander said on Friday, but Russia said army units had already done so near the city of Deir al-Zor.

FILE PHOTO: A view shows damaged buildings in Deir al-Zor, eastern Syria February 19, 2014. REUTERS/Khalil Ashawi/File Photo

An aide to President Bashar al-Assad meanwhile said the government would fight any force, including U.S.-backed militias, in efforts to recapture the rest of the country.

Syrian government forces supported by Russian air strikes and Iran-backed militias, and a U.S.-backed alliance of Kurdish and Arab fighters, are converging on Islamic State in separate offensives around Deir al-Zor.

The government side has advanced into the city from the west. Last week, they broke an Islamic State siege of the provincial capital, which sits on the western bank of the river.

The Deir al-Zor military council, fighting as part of the U.S.-backed Syrian Democratic Forces (SDF), has meanwhile advanced toward Deir al-Zor from the eastern side of the river since launching an offensive into the province a week ago.

Military council commander Ahmed Abu Khawla warned government forces and their militia allies against firing across the river as his fighters close in -- something he said had happened in recent days.

“Now we have 3 km between us and the eastern riverbank, once our forces reach the area, any shot fired into that area we will consider an attack on the military council,” he said.

“We have notified the regime and Russia that we are coming to the Euphrates riverbank, and they can see our forces advancing,” he said. “We do not allow the regime or its militias to cross to the eastern riverbank.”

But Russian foreign ministry spokeswoman Maria Zakharova said the Syrian army had already crossed.

“The suburbs of this provincial center (Deir al-Zor) have been liberated. Advance units have successfully crossed the Euphrates and are holding positions on its eastern bank,” she said, without specifying where.

Abu Khawla said this was “mere propaganda ... no one has crossed.”

Assad aide Bouthaina Shaaban later said the Syrian government was ready to fight the SDF.

“Whether it’s the Syrian Democratic Forces, or Daesh (Islamic State) or any illegitimate foreign force in the country ... we will fight and work against them so our land is freed completely from any aggressor,” she said in an interview with Hezbollah’s Al Manar TV.

“I’m not saying this will happen tomorrow ... but this is the strategic intent,” she said, dismissing suggestions that Washington and Moscow’s military decisions would decide Syria’s fate.

The Russian- and U.S.-backed campaigns against Islamic State in Syria have mostly stayed out of each other’s way as the sides seek to avoid conflict, with the Euphrates often acting as a dividing line between the sides. Talks have been underway to extend a formal demarcation line that has separated the campaigns, officials have said.

The SDF accused Syrian government forces of attacking its positions near the town of Tabqa in Raqqa province and the United States shot down a Syrian government warplane in June.

Abu Khawla said a civilian administration would be set up to run areas of Deir al-Zor province captured from Islamic State by his fighters, including oil fields. The Syrian government was “not fit to lead and rule the people”, he said.

Oil-rich Deir al-Zor province is Islamic State’s last major foothold in Syria and Iraq. It is bisected by the Euphrates River and abuts Iraq.

“MOVING FORCEFULLY AND QUICKLY”

“Every village around the eastern riverbank of the Euphrates river until the Iraqi-Syrian border is a goal for our forces,” he said. “We are moving forcefully and quickly. We do not have a timeline, but we hope soon to free the entire eastern bank.”

Reflecting the demarcation line, the U.S.-led coalition said on Thursday the SDF was not planning to enter Deir al-Zor city.

But while Deir al-Zor city was not an SDF target, Abu Khawla did not rule out the possibility it may become one, saying people in the city wanted to be liberated from “the regime and Daesh at the same time”.

But “right now, we have a schedule that we’re following which is the liberation of the eastern riverbanks of the Euphrates”, he said.

He said Islamic State had “shown fierce resistance” when SDF fighters entered the outskirts of Deir al-Zor on the eastern bank. “The battles are continuous,” he said.

Abu Khawla, who is in his early 30s, said 10,000 fighters were taking part in the Deir al-Zor campaign, the bulk of them members of Arab tribes from eastern Syria. The campaign is supported by the Kurdish militia that dominate the SDF.

“All our soldiers’ training (is) in the Coalition training camps, they oversee our training and our armament,” he said.

Abu Khawla was a member of a Free Syrian Army rebel group in Deir al-Zor until Islamic State took over most of the province in 2014 at the height of its expansion in Syria and Iraq. He fled to Turkey before returning to Syria and joining the SDF.

“Now we are setting up a civil council parallel to the military council of Deir al-Zor, and this civilian council will run all areas freed from (Islamic State),” he said.