The claim of agreement with Washington came amid conflicting reports about Russia's intentions in Syria and whether it is targeting only Islamic State and al-Qaida-linked militants.
The U.S. and its allies fear that Russia, which has backed the family of President Bashar Assad since the current leader's father was in power, is using the air campaign as a pretext to go after anti-Assad rebels that include CIA-backed groups.
Russian jets appeared to be primarily bombing central and northwestern Syria, strategic regions that are the gateway to Assad's strongholds in the capital of Damascus and the coast.
Warplanes hit locations of a U.S.-backed rebel group, Tajamu Alezzah, in the central province of Hama, said the Britain-based Syrian Observatory for Human Rights. It added that Tajamu Alezzah also was targeted a day earlier.
Idlib province appeared to bear the brunt of the attacks, activists said. The province is controlled by a coalition of rebel groups that include the al-Qaida-linked Jabbat al-Nusra.
In Syria's chaotic civil war and rapidly shifting battlefield terrain, however, it can be difficult to distinguish which groups holds what territory.
On Wednesday, French Defense Minister Jean-Yves Le Drian said Russian warplanes "didn't hit Islamic State," and U.S. Defense Secretary Ash Carter had also said the Russians appeared to have targeted areas that did not include IS militants.
Speaking Thursday at the United Nations, Russian Foreign Minister Sergey Lavrov rejected suggestions that the airstrikes were to shore up support for Moscow's main ally in the Middle East.
He insisted Russia was targeting the same militant groups as the U.S.-led coalition, which is conducting its own airstrikes in Syria: the Islamic State, also known as ISIL, the al-Qaida-linked Jabbat al-Nusra and other groups.
"I would recall that we always were saying that we are going to fight ISIL and other terrorist groups," he said. "This is the same position which the Americans are taking. The representatives of the coalition command have always been saying that their targets are ISIL, al-Nusra and other terrorist groups. This is basically our position as well. We see eye-to-eye with the coalition on this one."
Lavrov added: "If it looks like a terrorist, if it acts like a terrorist, if it walks like a terrorist, if it fights like a terrorist, it's a terrorist, right?"
Asked if he agreed with Lavrov, U.S. Secretary of State John Kerry said: "Well, in concept."
Kremlin spokesman Dmitry Peskov acknowledged to reporters that, "Of course the goal is to help the Syrian army where it is weakest. Yes, that is right. The weak points are where the Syrian army is fighting against IS and other terrorist groups."
As concerns grew about a conflict that has now drawn in warplanes from the world's two most powerful militaries, Russian President Vladimir Putin denied reports that civilians were killed in any Russian airstrikes.
"We are ready for such information attacks," he said in a live broadcast from the Kremlin. "The first reports of civilian casualties came even before our jets took off."
Lt. Gen. Robert Otto, deputy chief of staff for intelligence and surveillance for the Air Force, said the Russians have been dropping "dumb bombs" — munitions that are not precision-guided. The use of such indiscriminate targeting could lead to the deaths of innocent civilians, he said, and create more terrorists than they kill.
One of the airstrikes hit near a mosque in the city of Jisr al-Shughour, which fell in April to rebel groups including al-Nusra, the Observatory said. A video showed damage to the mosque and a man could be heard saying that one person was killed.
The Pentagon began talks via video teleconference with Russian military officials on ways to avoid U.S. and Russian forces firing on each other in Syria.
Otto said that even as the U.S. tries to ensure Russian airstrikes don't conflict with coalition operations in Syria, he does not believe there will be any real intelligence-sharing with Moscow.
"I have a low level of trust in the Russians. It's trust but verify," he said. "It's easy, then, to exchange factual data where you're going to operate. I would not envision a relationship where I would share some of my intelligence with them."
Russian Defense Ministry spokesman Igor Konashenkov said its aircraft damaged or destroyed 12 targets in Syria belonging to the Islamic State group, including a command center and two ammunition depots. Officials acknowledged, however, that other unidentified groups were being targeted as well.
Konashenkov said Russian Su-24M and Su-25 jets flew 20 sorties since Wednesday, and he insisted civilian areas were not targeted. He later said Su-34s also had flown missions.
Hundreds of Chechens and Central Asian fighters have joined the battles in Syria since the early days of the civil war, and many form the backbone of al-Nusra and Islamic State. Some of those Chechen extremists are part of the coalition that controls Idlib.
Putin has said Russia would be fighting "gangs of international terrorists." The Syrian government uses the word "terrorists" to describe all rebel groups.
The U.S. and Russia agree on the need to fight IS but not about what to do with Assad. The Syrian civil war, which grew out of an uprising against the longtime leader, has killed more than 250,000 people since March 2011 and sent millions fleeing elsewhere in the Middle East and Europe.
Lavrov also said Russia did not plan to carry out airstrikes against IS militants in Iraq, which has seen large parts of its territory overrun by the extremists. "We are polite people, we don't come if not invited," Lavrov said.
With U.S. and allied airstrikes daily, and now Russian warplanes in Syrian airspace, the war is taking on a dangerous new dimension.
In Paris, Russian Ambassador Alexander Orlov said Russian officials warned the Americans "via confidential channels" of where they planned to strike. He also noted a coordination center was being set up in Baghdad that would include Syrians, Iraqis, Iranians and Russians — and any other country that wants to participate.
Iran's Foreign Ministry said it fully supports Russian airstrikes against "terrorist groups" in Syria.
The "Islamic Republic of Iran considers military action by Russia against armed terrorist groups to be a step toward fighting terrorism and toward resolving the current crisis" in Syria, said ministry spokeswoman Marzieh Afkham in a statement carried by the official IRNA news agency.