The strikes reportedly hit rebel-controlled areas of Homs and Hama provinces, causing casualties.
The US says it was informed an hour before they took place.
Russian defense officials say aircraft targeted the Islamic State (ISIS) group, but an unnamed US official told Reuters that so far they did not appear to be targeting ISIS-held territory.
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 its ally remaining in power.
The upper house of the Russian parliament granted President Vladimir Putin permission to deploy the Russian air force in Syria.
The Russian defense ministry said the country’s air force had targeted ISIS military equipment, communication facilities, arms depots, ammunition and fuel supplies.
A Syrian opposition activist network, the Local Co-ordination Committees, said Russian warplanes hit five towns – Zafaraneh, Rastan, Talbiseh, Makarmia and Ghanto – resulting in the deaths of 36 people, including five children.
None of the areas targeted were controlled by ISIS, activists said.
In a TV address, 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.
Vladimir Putin added that Russia was not going to send ground troops to Syria, and that its role in Syrian army operations would be limited.
“We certainly are not going to plunge head-on into this conflict… we will 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.
A US defense official said: “A Russian official in Baghdad this morning informed US embassy personnel that Russian military aircraft would begin flying anti-ISIL [ISIS] missions today over Syria. He further requested that US aircraft avoid Syrian airspace during these missions.”
State department spokesman John Kirby told reporters: “The US-led coalition will continue to fly missions over Iraq and Syria as planned and in support of our international mission to degrade and destroy ISIL [ISIS].”
The US House Ethics Committee has voted to release its report on former Republican Representative…
ABC News has agreed to pay $15 million to President-elect Donald Trump to settle a…
South Korea’s parliament has voted to impeach President Yoon Suk Yeol over his failed attempt…
Israeli war planes have carried out more than 100 air strikes in Syria on December…
President-elect Donald Trump has threatened to impose 100% tariffs on the BRICS countries if they…
Syrian troops have withdrawn from the city of Aleppo following an offensive by rebels opposed…