The UN Security Council held an emergency meeting overnight at the request of the Kremlin
Russia has accused the US-led coalition in Syria of being on the "boundary between criminal negligence and direct connivance with Islamic State terrorists".
The stinging attack comes after the US admitted leading a coalition airstrike which reportedly killed up to 80 Syrian soldiers in the east of the war-torn country.
Russia's foreign ministry said the strike jeopardised a fragile American-Russian brokered ceasefire in Syria.
It added that the strike was a result of Washington's "stubborn refusal" to cooperate with Moscow in fighting Islamic State and other terror groups.
The Syrian military called the strike a "serious and blatant attack on Syria and its military" and "firm proof of the US support of Daesh and other terrorist groups", using the Arabic acronym for IS.
The airstrike hit a base in the eastern city of Deir el-Zour, which is surrounded by Islamic State militants.
Russia's defence ministry said more than 60 Syrian soldiers were killed and around 100 wounded in four strikes by two F-16s and two A-10s.
The Syrian Observatory for Human Rights, a British-based monitoring group with contacts across Syria, cited a military source at Deir el-Zour airport as saying at least 80 Syrian soldiers died.
A senior White House official said the US has relayed "regret" through the Russian government for the unintentional loss of life to Syrian forces.
US Central Command said the strike was immediately halted "when coalition officials were informed by Russian officials that it was possible the personnel and vehicles targeted were part of the Syrian military".
A US military official told Reuters news agency the strike was carried out using US intelligence, and added that the possible targets had been followed for days.
Meanwhile, Australia's defence ministry has confirmed that its aircraft "were among a number of international aircraft taking part in this Coalition operation".
In a statement, the ministry said that "bombing ceased immediately" after the operations centre was informed by Russia that targets may have been Syrian military personnel.
The ministry offered its "condolences to the families of any Syrian personnel killed or wounded" and said it will cooperate fully with the US review into the incident.
UN Security Council
The Syrian military said the damage caused by the strike has allowed the IS extremists to advance their position on to a hill overlooking the base.
Three tanks, three infantry fighting vehicles, four mortars and an anti-aircraft gun were destroyed, a Syrian military spokesman said according to Russia's TASS news agency reported.
Following the strike, the UN Security Council held an emergency meeting overnight at the request of the Kremlin.
The US ambassador to the UN, Samantha Power, rebuked Russia for the move.
"Russia really needs to stop the cheap point scoring and the grandstanding and the stunts and focus on what matters, which is implementation of something we negotiated in good faith with them," Ms Power said.
She said the US was investigating the airstrike and "if we determine that we did indeed strike Syrian military personnel, that was not our intention and we of course regret the loss of life".
When asked if the incident spelled the end of the Syria deal between Moscow and Washington, Russia's UN Ambassador Vitaly Churkin said: "This is a very big question mark.
"I would be very interested to see how Washington is going to react. If what Ambassador Power has done today is any indication of their possible reaction then we are in serious trouble."
He said he had never seen "such an extraordinary display of American heavy-handedness" as displayed by Ms Power at the acrimonious meeting.
The fragile ceasefire brokered by the US and Russia has largely held for five days, despite dozens of alleged violations on both sides.
It began on Monday, but aid convoys have been unable to enter rebel-held parts of the city of Aleppo - a key part of the deal.
Russian President Vladimir Putin has already questioned US commitment to the ceasefire, claiming Washington was not prepared to break with "terrorist elements" battling Bashar al Assad's forces.