Russia and US military will hold talks “as soon as possible” to avoid clashing in Syria, the countries’ top diplomats say.
Russian defense officials say their aircraft carried out about 20 missions against the so-called Islamic State group (ISIS) on September 30.
However, the US expressed fears the targets were non-ISIS opponents of Russia’s ally, Syrian President Bashar al-Assad.
The US is targeting ISIS with air strikes in both Syria and Iraq.
NATO said there had been little co-ordination by Russia with US-led forces against ISIS, also known as Isil. The US says it was informed of Wednesday’s air strikes only an hour before they took place.
The New York Times and the Wall Street Journal report that US-backed rebels were targeted by Russia.
Russia’s Foreign Minister, Sergei Lavrov, said there was a need to “establish channels of communication to avoid any unintended incidents”. His US counterpart, John Kerry, said talks will be held “as soon as possible,” maybe as early as October 1.
John Kerry added: “It’s one thing to be targeting Isil, but the concern, obviously, is that this is not what was happening.”
France’s Defense Minister, Jean-Yves Le Drian, told French lawmakers: “Curiously, they didn’t hit Islamic State. I will let you draw a certain number of conclusions yourselves.”
Syria’s civil war has raged for four years, with an array of armed groups fighting to overthrow the government.
The US and its allies have insisted that President Bashar al-Assad should leave office, while Russia has backed him remaining in power.
The Russian defense ministry said the country’s air force had targeted ISIS military equipment, communication facilities, arms depots, ammunition and fuel supplies – and did not hit civilian infrastructure or areas nearby.
Syrian opposition activists said Russian warplanes hit towns including Zafaraneh, Rastan and Talbiseh, resulting in the deaths of at least 36 civilians, a number of them children.
None of the areas targeted was controlled by ISIS, activists said.
In a TV address, Russian President Vladimir Putin said the air strikes were targeting Islamist militants – including Russian citizens – who have taken over large parts of Syria and Iraq.
“If they [militants] succeed in Syria, they will return to their home country, and they will come to Russia, too,” he said.
He added that Russia would be “supporting the Syrian army purely in its legitimate fight with terrorist groups”.
Vladimir Putin also said he expected President Bashar al-Assad to talk with the Syrian opposition about a political settlement, but clarified that he was referring to what he described as “healthy” opposition groups.