The first group of Russian planes left Hmeymim air base in Syria on Tuesday morning, the Russian Defense Ministry said.
Russia's surprise announcement Monday that it would begin withdrawing its forces from the conflict came as suddenly as its devastating airstrike campaign that started in September.
But Syria's government was not caught unawares by the move, a senior official told CNN.
"We knew beforehand that this is what was going to be announced because the Russians came here to achieve certain jobs, and we and they agreed that most of the jobs have been achieved."
In terms of "fighting terrorism," she said, "they've done a great job and they will continue in fighting terrorism, but there are some tasks which have been completed, and therefore the Russian and Syrian leadership agreed that it is appropriate now to withdraw some of the planes or forces."
Russian President Vladimir Putin
announced the withdrawal Monday, saying that "the task that was assigned to the Ministry of Defense and the armed forces as a whole has achieved its goal."
But critics said that Moscow's stated goal of fighting terrorist groups such as ISIS in Syria did not accurately reflect the reality of its military actions in the war-ravaged nation.
They point to the bombings of civilian areas
as evidence that Russia has been more interested in helping Assad eliminate his opposition.
Syrian opposition welcomes Russian drawdown
Asked Tuesday whether the Russian withdrawal signaled a case of "mission accomplished," Shaaban replied, "Hundreds of villages have been liberated, many towns have been liberated from armed gangs, huge parts of Syria have been liberated."
She said Russia's Defense Ministry had said the "war against terrorism will continue. And we are happy also to see Russian-American coordination in fighting terrorism."
Russia's steps were "the right steps toward a political settlement and also toward a continuation of fighting terrorism," she continued.
Putin's announcement came as Syrian peace talks resumed
Monday in Geneva, Switzerland, in which members of the Syrian regime and opposition are meeting indirectly through a mediator to try to forge a path to peace.
Speaking on the sideline of the talks Tuesday, Syria's main opposition group, the High Negotiations Committee, said it welcomed the Russian drawdown.
"What really keep(s) Assad in power now, what keep(s) crimes until this moment, is the presence of the Russian forces there," opposition group spokesman Salim al-Muslet told reporters.
"I believe if they (are) serious about pulling out ... it will be an end to crimes in Syria and will help us to put an end to terrorism there in Syria."
Putin "should put pressure on Assad to accept (the) outcome" of the Geneva talks, he said.
Russia has both economic and ideological reasons to support the Syrian regime, even as many other countries blame Assad for the deaths of thousands of dissidents.
Analysts estimate Syria has spent billions of dollars on Russian-made defense equipment
. And Russia doesn't believe revolutions or regime change can bring stability. It often points to the Arab Spring
and the U.S.-led war in Iraq as evidence.
So it's no surprise that Russia launched hundreds of airstrikes in support of Assad over the past few months.
In a phone call Monday between Putin and Assad, "the two leaders noted that the operations conducted by Russia's Aerospace Forces have brought about a real turnabout in the fight against the terrorists in Syria, throwing their infrastructure into disarray and causing them substantial damage," the Kremlin said.
"In this context, Mr. Putin said that Russia's Armed Forces have fulfilled their main mission in Syria
As for the Syrian President, Assad "noted the professionalism, courage and heroism of the Russian service personnel who took part in the military operations, and expressed his profound gratitude to Russia
for providing such substantial help in fighting terrorism and providing humanitarian assistance to the civilian population," the Kremlin said.
But while the Russian campaign is winding down, it will not be a complete drawdown.
Russia will maintain an aviation support center in Syria to monitor compliance with the ongoing cessation of hostilities
, the Kremlin said.
And a Russian military official told CNN the Kremlin was not ruling out continuing airstrikes.
Assad still has the support of two other allies: Iran and Hezbollah.
"Iran and their Shia militias, and Hezbollah, are the ground component to Russia's air involvement," Andrew Tabler of the Washington Institute for Near East Policy
Understanding Putin's motivations
The benefits of Russia staying in Syria no longer outweighed the costs, said James Gelvin, a history professor at the University of California, Los Angeles.
And with Russia's economy in trouble because of falling oil prices, the fight in Syria could be deemed an unnecessary cost.
Barry Strauss, a history professor at Cornell University, said Putin's strategic goal had been to weaken NATO, by presenting Moscow as a more reliable regional power than Washington in Eastern Europe and the Mediterranean.
"By helping their friend in Syria without getting bogged down in a quagmire, Russia offers quite a contrast to American policy in the region," Strauss said.
"Assad now goes into peace takes with a much stronger hand, thanks to Russia, but he also knows not to take Russian aid for granted."
Keeping some level of military presence in the country also allowed Russia to continue pressuring regional rival Turkey, he said.
"Catching the Americans flatfooted and flabbergasted by the start of their partial withdrawal only sweetens Russia's moment," he said.
Richard Haass, president of U.S. think tank the Council on Foreign Relations, said Putin's aim had not been to help his ally regain control of the entire country, but to shore up his power and strengthen his hand ahead of political negotiations.
"It seems to have essentially shored him up, strengthened him, and now you begin a political process against a much lower-key military process," he told CNN.
"I think it allows Assad in some ways to relax."
The timing of Russia's withdrawal is significant for two reasons.
First, Putin's announcement came the same day as peace talks resumed
in Geneva. On the agenda: how to govern Syria, a new constitution and presidential elections.
Some see Russia's withdrawal as evidence that Putin is sending a message that Syria must reach a political solution, CNN's Moscow correspondent Matthew Chance said.
"You can't ignore the timing of this and the symbolism," he said.
German Foreign Minister Frank-Walter Steinmeier also said Assad would face new pressure.
"If a Russian troop withdrawal materializes, it would put President Assad under pressure to finally seriously negotiate a peaceful political transition in Geneva that would ensure the continuation of a Syrian state," he said.
Staffan de Mistura, U.N. special envoy to Syria, welcomed Russia's withdrawal.
He called it "a significant development, which we hope will have a positive impact on the progress of the negotiations in Geneva aimed at achieving a political solution of the Syrian conflict and a peaceful political transition in the country."
The second reason Russia's timing is significant: This week marks the fifth anniversary of the Syrian civil war
More than 270,000 people have been killed, half the country has been uprooted, and more than a million migrants have made the dangerous voyage to Europe, leading to an international humanitarian crisis.
The war has taken an especially brutal toll on children.
At least 900 children were killed last year -- "150 of them while they were sitting in their own schools," de Mistura has said.
And with much of the country reduced to rubble, about half of all Syrian children -- 2.8 million -- don't have access to education, according to UNICEF, the U.N. children's agency.
The agency said children as young as 3 are working or begging to help sustain their families.