A Russian foreign ministry spokesman said any such action, without the backing of the UN, would be “an act of aggression”.
It comes as US Secretary of State John Kerry meets Arab leaders in Saudi Arabia to try to build a coalition against Islamic State (IS) militants.
President Obama has threatened action against IS in Syria as well as Iraq.
IS controls large parts of Syria and Iraq after a rapid military advance.
In a speech outlining his strategy, Mr Obama said any group that threatened America would “find no safe haven”.
He also announced that 475 US military personnel would be sent to Iraq but said they would not have a combat role.
But the statement brought a strong reaction from Russia, which has been an ally of embattled Syrian President Bashar al-Assad.
“The US president has spoken directly about the possibility of strikes by the US armed forces against Isil (IS) positions in Syria without the consent of the legitimate government,” ministry spokesman Alexander Lukashevich was quoted as saying.
“This step, in the absence of a UN Security Council decision, would be an act of aggression, a gross violation of international law.”
Syria also repeated its warning that the US had to co-ordinate with the Syrian government before launching air strikes on its territory.
“Any action of any kind without the consent of the Syrian government would be an attack on Syria,” National Reconciliation Minister Ali Haidar said on Thursday.
Last month Syria offered to help the US fight Islamic State, however the US ruled that out.
The US has launched more than 150 air strikes against the group in Iraq and has provided arms to Iraqi and Kurdish forces fighting against IS.
The jihadist group has become notorious for its brutality, recording their beheadings of enemy soldiers and Western journalists.
Mr Kerry, who arrived in the Red Sea port of Jeddah on Thursday, will hold talks with representatives of Saudi Arabia and other oil-rich Gulf states as well as Egypt, Jordan, Iraq, Lebanon and Nato member Turkey.
Reports say that among the issues to be discussed are training for Syrian rebels on Saudi soil and broader permission from regional states to use their airspace in order to increase the capacity of US aircraft.
In a 15-minute speech shown at peak time in the US on Wednesday, President Obama vowed that America would lead “a broad coalition to roll back” IS.
“Working with the Iraqi government, we will expand our efforts beyond protecting our own people and humanitarian missions, so that we’re hitting Isil targets as Iraqi forces go on the offense,” he said.
President Obama was elected in part because of fervent opposition to the 2003 invasion of Iraq, and presided over the US troop pullout from the country.
Last year, President Obama abandoned plans to launch airstrikes in Syria against government forces after congressional opposition.
In his speech, he ruled out working with President Bashar al-Assad of Syria, despite the fact that his forces are also engaged in fighting IS.
Instead, he said, the US would seek to strengthen the non-IS Syrian opposition, which fights against both IS and President Assad.
Syria’s Western-backed National Coalition welcomed Mr Obama’s plan, and urged Congress to approve it.
However, the BBC’s Jim Muir in northern Iraq says the Syrian opposition is fragmented and dominated by Islamists, who may be opposed to IS but are seeking Islamic rule rather than democracy.
Kerry ridicules Russian talk of intl law
US Secretary of State John Kerry labelled as laughable today Russian claims that a US campaign against the Islamic State is unilateral and violates international law.
“I must say if it weren’t so serious what’s happening in Ukraine one might almost laugh at the idea of Russia raising the issue of international law or any question of the UN,” Kerry told reporters.
“I am really rather surprised that Russia would dare to assert any notion of international law after what has happened in Crimea and eastern Ukraine,” Kerry added.
BBC and Business Standard
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