US President Barack Obama has said the Russian bombing campaign in Syria in support of President Bashar al-Assad is driving moderate opposition underground and "only strengthening" Islamic State.
Mr Obama said he rejected the Russian assertion that all armed opponents of Mr Assad were terrorists.
Moscow insists its air strikes - now in their third day - are targeting IS.
But the Syrian opposition and others have suggested non-IS rebels are bearing the brunt of Russian attacks.
"The problem here is Assad and the brutality that he's inflicted on the Syrian people, and it has to stop," Mr Obama said.
"We're not going to co-operate with a Russian campaign to destroy anyone who is disgusted and fed up with Assad."
Russia steps up strikes
Russia has stepped up its campaign of air strikes against opponents of Syrian President Bashar al-Assad.
Moscow said its aircraft had "conducted 18 sorties on 12 positions held by the Islamic State (IS) terrorist group in Syria" since Thursday.
Targets included the IS stronghold of Raqqa, but also Aleppo, Hama and Idlib - provinces with little IS presence.
Members of the US-led coalition targeting IS have renewed their criticism of the Russian action.
In a statement, the US, UK, Turkey and other coalition members called on Russia to cease air strikes they said were hitting the Syrian opposition and civilians, adding that they would "only fuel more extremism".
The Syrian opposition and others have suggested non-IS rebel factions opposed to President Assad - the Kremlin's ally - are bearing the brunt of the Russian attacks.
Alexei Pushkov, the head of the foreign affairs committee in Russia's parliament, said the air strikes - which began on Wednesday - could last for three to four months.
He added that the US had only "pretended" to bomb IS, and promised that Russia's campaign would be much more effective.
The British-based Syrian Observatory for Human Rights said the latest Russian air strikes had hit a training camp and a camouflaged command post near the IS "capital" of Raqqa, and that 12 IS fighters were killed in the attack.
Activists and residents of the city said IS had cancelled Friday prayers and emptied mosques, amid fears of further Russian air strikes.
Elsewhere, a radio mast and communications tower belonging to the Free Syrian Army - forces opposed to President Assad which have received American training and supplies - were attacked by Russian aircraft in Aleppo. However, Syrian sources said neither had been destroyed, contrary to earlier reports.
Meanwhile, IS fighters have attacked a government airbase in eastern Syria.
Reports from the area, near the IS-controlled city of Deir al-Zour, speak of loud explosions, heavy clashes and government fighter jets circling in the sky.
The US-led coalition said it had targeted IS in 28 air strikes in both Syria and Iraq on Thursday.
The warning from members of the US-led coalition came as the French and Russian presidents met in Paris. The meeting was called to discuss peace efforts in Ukraine, but were overshadowed by Syria.
An aide to French President Francois Hollande said he and Russian President Vladimir Putin said they had "tried to narrow differences" over Syria during talks that lasted more than an hour.
The strikes in Syria are Russia's first military engagement outside the borders of the former Soviet Union since the end of the Cold War.Russian Foreign Minister Sergei Lavrov, speaking at the UN in New York, said Russia would also fight other terrorist groups including the al-Nusra Front - an al-Qaeda affiliate.
He said this position was the same as that of the US-led coalition, which has been carrying out air strikes in Iraq and Syria for the past year.
"We are not supporting anyone against their own people. We fight terrorism," he said.
Mr Lavrov said the targets were selected "in co-ordination with the Syrian army".
Syrian Foreign Minister Walid Muallem, speaking at the same meeting, said air strikes alone were not enough to defeat IS but described the Russian action as "effective'' because it supported his country's efforts to combat terrorism.
He also said his country's army was "capable of cleansing the country of those terrorists".