Each ship is capable of carrying up to 300 marines and a dozen tanks, according to Russian media reports. That would make it the largest known Russian troop deployment to Syria, signaling that Moscow is becoming increasingly uneasy about Syria's slide toward civil war.
Russia has been Syria's strongest ally over the course of the uprising, which began in March 2011 with mostly peaceful protests against Assad's regime. A ferocious government crackdown led many to take up arms, and the conflict is now an armed insurgency.
Opposition groups say more than 14,000 people have been killed since the Syrian uprising began in March 2011, including more than 3,400 security forces.
Syria is Russia's last remaining ally in the Middle East, and has been a major customer of Soviet and Russian weapons industries for the last four decades, acquiring billions of dollars worth of combat jets, helicopters, missiles, armored vehicles and other military gear.
Tartus is Russia's only naval base outside the former Soviet Union, serving Russian navy ships on missions to the Mediterranean and hosting an unspecified number of military personnel.
Monday's renewed shelling in the restive Homs province comes as regime forces carry out an offensive to drive out rebels by shelling urban areas with tanks and attacking from helicopters. Rebels also have attacked Syrian forces, mostly trying to burn tanks.
The violence comes one day after the head of the U.N. observers' mission demanded that warring parties allow the evacuation of women, children, elderly and sick people.
"There is renewed shelling and shooting in the city of Homs," said the Britain-based Syrian Observatory for Human Rights, an activist group that cited witnesses on the ground.
Gunfire and explosions also were reported in Homs, the Observatory said.
On Saturday, the U.N. said its 300 observers based in Syria were suspending all missions because of concerns for their safety after fighting intensified over the previous 10 days. But the monitors said they were remaining in Syria in Damascus.
The conflict in Syria has brought broad international condemnation, but the regime has appeared largely impervious to the pressure.
U.S. Sen. John McCain on Sunday characterized the lack of American aid to Syrian rebels as "shameful" and said helping their cause would deal "the greatest blow to Iran in the Middle East in 25 years." His remarks sought to maintain political pressure on President Barack Obama as violence in the region escalated.
"The fact that the United States of America is not helping these people and we can is shameful," McCain, who ran against Obama in 2008, said Sunday on NBC's "Meet the Press."
So far, the U.S. has refused to arm Syrian rebels in part to avoid a proxy fight with Iran and Russia, which both back Assad's regime.