There was no immediate comment from Moscow or Damascus.
The Euphrates slices diagonally across the province, an oil-rich eastern region bordering Iraq.
According to the Syrian Observatory for Human Rights, the latest development comes in the framework of the regime forces' attempts to encircle and besiege Deir al-Zour before advancing on the eastern countryside of the city along the western bank of the river.
"Several SDF fighters were wounded".
The simultaneous advancements against Daesh have raised concerns of clashes between SDF and the Syrian troops.
Deir el-Zour is the militants' last major urban stronghold in Syria and is home to almost 100,000 residents. Russian Defense Ministry Spokesman Major General Igor Konashenkov has called on the US-led worldwide coalition and the opposition supported by it not to hamper the actions of the Syrian government forces against terrorists.
He added, however, that as the two groups converge on the Islamic State position from opposite sides, it will get more hard to stay out of each other's way. He says the levels of those talks have also varied, with some including ground-level commanders.
The U.S. coalition has said the SDF does not plan to enter Deir al-Zor city, where Syrian soldiers have broken an Islamic State siege that lasted since 2014.
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The military base is seen as a valuable asset for the Syrian army as it presses its campaign against Islamic State in Deir al-Zor province.
The London-based watchdog group added that the forces crossed the river using water bridges following intense shelling on IS positions in the eastern bank of the river.
A USA official told CNN that the intent was to shift the de-confliction conversations and focus them to be more tactical, sharing where ground forces were located to prevent any accidental targeting. "We have asked for explanations from the coalition. and necessary action to stop these jets".
Diplomat Alexey Goltyaev says the 14th Commission of Inquiry report on Syria "doesn't contain a single word about war crimes committed by the US military and its coalition partners during the storming of Raqqa" to battle Islamic State militants. On Friday, he warned the army and its allies against firing across the river, which he said they had done in recent days. "As soon as the Syrian government troops began to cross the river, water level in the Euphrates rose within hours and the current velocity almost doubled to two meters per second", he said.
"I'm not saying this will happen tomorrow. but this is the strategic intent", Bouthaina Shaaban said in a TV interview.
The Syrian army sealed off Deir Az Zor on three sides as of Monday, but ISIL still controls eastern districts along the river, which both the group and civilians had used as an escape route.
Shi'ite militias fighting with Damascus also launched attacks against Islamic State in the south of Deir al-Zor province along the border.