The U.S. and Russian military will hold talks "as soon as possible" to avoid clashing in Syria, the countries' top diplomats say, according to BBC News.
Russian defence officials say their aircraft carried out about 20 missions against the so-called Islamic State group (IS) on Wednesday, September 30.
But the U.S. expressed fears the targets were non-IS opponents of Russia's ally, Syrian President Bashar al-Assad.
The U.S. is targeting IS with air strikes in both Syria and Iraq.
Nato said there had been little co-ordination by Russia with U.S.-led forces against IS, also known as Isil. The U.S. 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 U.S.-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 U.S. counterpart, John Kerry, said talks will be held "as soon as possible," maybe as early as Thursday.