Russia is a leading backer of Syria's President Bashar Assad and rebels fighting to topple his regime have previously targeted the diplomatic mission in Damascus with rockets and mortars.
In Moscow, the Russian Foreign Ministry confirmed the attack, saying rebels fired mortars that landed on the grounds of their embassy. Three workers were injured in the attack, the ministry said, adding that the injuries were not life-threatening. It gave no further details.
The Russian Embassy is located in Damascus' upscale Mazraa district, which also houses several Syrian security institutions, a soccer stadium and nightclubs.
In another mortar attack outside the capital, two people were injured when shells slammed into a residential building in the suburb of Jaramana, SANA said.
The attacks come as diplomatic wrangling continues over how to collect Syria's arsenal of chemical and biological agents to prevent any repeat of the Aug. 21 attack outside Damascus that, according to the U.S., contained chemical agents and killed more than 1,400 people, including 400 children.
Activist groups estimate the death toll of the attack that brought Washington to the brink of a military strike against Syria to be significantly lower. Assad's government accuses rebels of using the chemical weapons.
Last week, a U.N. report confirmed the use of sarin in the August attack outside Damascus. Russia blamed the rebels, while the U.S. and its European and Arab allies said Assad's forces were responsible.
On Sunday, Russian Foreign Minister Sergey Lavrov said Moscow was ready to send military observers to Syria to ensure security for efforts to eliminate Syria's chemical weapons.
But the Russian official said his country is not considering sending a full military contingent.
Under a U.S.-Russian plan, Syria is to give up its chemical weapons. Security is one of the plan's major challenges, including how to prevent theft of the weapons.
In an interview broadcast Sunday on state TV's Channel One, Lavrov said Russia has proposed that there be an international presence on the perimeter of all areas where chemical weapons experts will work in Syria. "We are ready to share our servicemen and military police to participate in these forces," but "it seems to me that military observers will be sufficient," he said.
Although Russia and the U.S. worked together on the chemical weapons plan, Washington and Moscow remain at odds over several aspects of the Syrian crisis.
The United States, along with France, has sought a U.N. Security Council resolution that would authorize the use of force, if Syria reneges on the chemical weapons agreement, but Russia opposes invoking the U.N. Charter's Chapter 7 which would allow force.
Lavrov criticized what he called "impudent" attempts by the West to include that chapter in the resolution.
The minister said the West is unable to admit that previous military interventions, such as in Iraq and Libya, led to severe problems.
"They are primarily interested in the evidence of their own superiority. And is not the task that drives us - to solve the problem of chemical weapons in Syria," he said.
On the front lines inside Syria, anti-regime activists reported clashes between rebels and army troops in the southern province of Daraa and around the contested northern city of Aleppo. In its daily round up of the fighting, the Britain-based Syrian Observatory for Human Rights noted two regime air raids on the Damascus district of Jobar, an area from which rebels have been trying to storm the capital for months.
Rebels also battled Assad's troops in opposition strongholds near the capital, including in Zamalka, eastern Ghouta, Moadamiya and Yarboud and in several areas along the southern highway leading into Damascus, the Observatory said. There were no immediate reports of casualties in Sunday's fighting.
More than 100,000 people have been killed since the conflict started in March 2011. Millions have fled their homes, seeking shelter in safe parts of their homeland or in the neighboring countries of Lebanon, Jordan, Turkey and Iraq.
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