NATO also predicted Assad's fall, with Secretary-General Anders Fogh Rasmussen saying the regime's collapse is "only a matter of time."
"An opposition victory can't be excluded, unfortunately, but it's necessary to look at the facts: There is a trend for the government to progressively lose control over an increasing part of the territory," Russian Deputy Foreign Minister Mikhail Bogdanov said during hearings at a Kremlin advisory body.
Bogdanov also said Moscow is preparing to evacuate thousands of its citizens from Syria, where nearly two years of violent conflict have killed more than 40,000 people and turned Assad into a global pariah. His statement marks a clear attempt by the Kremlin to begin positioning itself for Assad's eventual defeat at a time when rebels are making significant gains.
Opposition fighters have seized large swaths of territory in northern Syria along the border with Turkey and appear to be expanding their control outside of Damascus, pushing the fight closer to Assad's seat of power in the capital. In a Damascus suburb, a bomb blast Thursday near a school killed 16 people, at least half of them women and children, the state news agency SANA reported.
A day earlier, the U.S., Europe and their allies recognized the newly reorganized opposition leadership, giving it a stamp of credibility and possibly paving the way for greater international aid to those fighting Assad's forces.
At the same time, international condemnation of the regime has grown more intense as Western officials raise concerns that Assad might unleash his chemical weapons stockpiles against rebels in an act of desperation. On Wednesday, the U.S. and NATO said Assad's forces had fired Scud missiles at rebel areas.
Syria denied the Scud allegations, calling them nothing more than a conspiracy.
But the NATO secretary-general said the military alliance detected the launch of a number of the unguided short-range missiles inside Syria earlier this week.
"We can't confirm details of the missiles, but some of the information indicates they were Scud-type missiles," he said at NATO headquarters in Brussels.
"In general, I think the regime in Damascus is approaching collapse. I think now it's only a question of time."
Fyodor Lukyanov, the editor of the magazine Russia in Global Affairs, said Bogdanov's statement may reflect new information about the situation on the ground.
"A public statement like that appears to indicate that the balance is shifting," he said.
Abu Bilal al-Homsi, an activist based in a rebel-held neighborhood of Homs in central Syria, said he is encouraged by Bogdanov's comments because Russia is in a position to know about the strength of Assad's forces.
"The Russians know his capabilities and his military force. Russia knows what warplanes and what weapons he has," Abu Bilal said via Skype. "The Free Syrian Army is on the verge of strangling Damascus and this indicates that the regime is reaching an end," he added, referring to the main rebel fighting force.
Despite Russia's acknowledgement that Assad could lose, Bogdanov gave no immediate signal that Russia would change its pro-Syria stance at the U.N. Security Council, where Moscow has shielded Damascus from world sanctions.
Bogdanov also reaffirmed Russia's call for a compromise, saying it would take the opposition a long time to defeat the regime and Syria would suffer heavy casualties.
"The fighting will become even more intense, and you will lose tens of thousands and, perhaps, hundreds of thousands of people," he said. "If such a price for the ouster of the president seems acceptable to you, what can we do? We, of course, consider it absolutely unacceptable."
Russia's ties to Syria date back to Assad's father, Hafez, who ruled Syria with an iron fist from 1971 until his death in June 2000. In the last four decades, Russia has sold Syria billions of dollars' worth of weapons. A change in power in Damascus could not only cost Russia lucrative trade deals, but also reduce Russian political influence in Arab world.
The Russians also strongly oppose a world order dominated by the United States and they are keen to avoid a repeat of last year's NATO air campaign that led to the ouster of Libyan leader Moammar Gadhafi, a former Moscow ally.
Bogdanov's remarks will likely be seen in Damascus as a betrayal of these longstanding ties. There was no immediate reaction from the Syrian regime on the comments.
Bogdanov said the Foreign Ministry is preparing evacuation plans for thousands of Russian citizens, most of whom are Russian women married to Syrian men and their children.
"We are dealing with issues related to the preparation for evacuation," Bogdanov said. "We have mobilization plans. We are finding out where our citizens are."
The Interfax news agency said that if the government decides to evacuate Russians from Syria, it could be done by ships escorted by the Russian navy and by government planes.
At the same time, violence was escalating in and around the capital.
The government says the bombing on Thursday in the Damascus suburb of Qatana was the latest in a string of similar bombings in and around Damascus that killed at least 25 people in the last two days.
The government blames the bombings on terrorists, the term it uses to refer to rebel fighters. While no one has claimed responsibility for the bombings, some have targeted government buildings and killed officials, suggesting that rebels who don't have the firepower to engage Assad's elite forces in the capital could be resorting to guerrilla measures.
Similar attacks hit four places in and around Damascus on Wednesday. Three bombs collapsed walls of the Interior Ministry building, killing at least five people. One of the dead was Syrian parliament member Abdullah Qairouz, SANA reported.
Assigning responsibility for the blasts remains difficult because rebels tend to blame attacks that kill civilians on the regime without providing evidence while competing groups often claim successful operations.
Isachenkov reported from Moscow. AP writers Ben Hubbard and Bassem Mroue in Beirut and Slobodan Lekic in Brussels contributed to this report.