The evacuation was the strongest sign yet of Moscow’s waning confidence in the ability of its ally President Bashar Assad to hold onto power. The U.N. chief said Tuesday that a diplomatic conclusion to the war seems unlikely.

U.S. State Department spokeswoman Victoria Nuland said the Russian evacuations indicate “the continued deterioration of the security situation and the violence that Assad is leading against his own people.”

Four buses carrying about 80 people, mostly women and children, crossed out of the country over land into neighboring Lebanon in the early afternoon. They were bound for the Lebanese capital Beirut to fly home in two planes that Russia sent. They apparently were not flown directly home out of Damascus because of the fighting around the airport there.

Russian announced the beginning of the evacuations on Monday, saying it would take out 100 nationals. The Russian Foreign Ministry says there are tens of thousands of Russians living in Syria. Many of them are Russian women married to Syrian men.

The officials said thousands more evacuations could follow – possibly by both air and sea.

Russia has been Assad’s main ally since the Syrian uprising began in March 2011, selling arms, providing technical support and, along with China, using its veto power in the U.N. Security Council to shield Damascus from international sanctions over the Syrian regime’s brutal crackdown on dissent.

But in recent months, Russia has started distancing itself from Assad. President Vladimir Putin said last month that he understands Syria needs change and that he was not protecting the Syrian ruler.

The Russians entered Lebanon at the Masnaa border crossing, where an official from their embassy in Beirut was waiting for them.

Some inside the buses closed the curtains so they would not be seen by journalists waiting at the border. Most refused to comment and those who did speak said only they were going home to visit relatives.

Jodie, an 8-year-old girl traveling from Damascus with her sister and her Syrian father said she was going to Moscow to see her mother, who is Russian. Jodie and her 4-year-old sister Nadine spoke briefly to reporters when they got off the bus to get their passports stamped at the border.

“I used to hear the shelling, but I was not scared,” said Nadine. “I would close my eyes.”

Officials at the Russian Embassy in Damascus said they have several thousand citizens registered as living in Syria. The officials, speaking on condition of anonymity because they were not authorized to talk to the media, said some of the people who were being evacuated Tuesday have lost their houses and need Russian government assistance to leave.

The officials downplayed the evacuation effort, denying that they are assisting their nationals’ departures from Syria because of the deteriorating security situation.

One of the officials, who identified herself only as the embassy’s head of protocol, said the government was simply responding to those who had asked for help in leaving Syria, suggesting they were mostly Russians living in areas where the fighting is fiercest.

“It’s their personal desire to leave Syria,” said the official. She noted that thousands of Russians were still in Syria.

In Moscow, Deputy Foreign Minister Andrei Denisov dismissed reports that the evacuations were the beginning of a Russian exodus from Syria. He told media there Russian planes landed in Beirut to deliver humanitarian aid at the Syrian government’s request, and would take home those who wanted to leave.

“There is no plan to take everyone out,” Denisov said. “Since the planes have arrived there, and some people with children want to leave, we are ready to take them out.”

As the evacuation got under way, Syrian government forces and rebels battled in the suburbs of Damascus and elsewhere.

The Britain-based Syrian Observatory for Human Rights said clashes between opposition fighters and troops were concentrated in the areas around the capital, including along the road linking it to the international airport.

Persistent fighting along the airport road has prompted regional and international airlines to suspend flights to Damascus in recent weeks, although Syrian officials maintain that the airport remains open.

International diplomacy has done little to ease Syria’s crisis, which according to the U.N. has claimed more than 60,000 lives since March 2011.

U.N. Secretary-General Ban Ki-moon said he didn’t see “much prospect of resolution” by diplomacy.

At his first news conference of the year, Ban noted the worsening humanitarian conditions inside Syria and for those who have fled to neighboring countries.

For months, special envoy Lakhdar Brahimi, who represents the U.N. and the Arab League, has been pushing for a cease-fire and the formation of a transitional government — with little apparent progress.

Ban said he and Brahimi reached a bleak conclusion after talks Monday.

“Our shared assessment is that we are still a long way from getting the Syrians together,” he said.