The main opposition group, the exiled National Coalition, has boycotted the talks while Syrian President Bashar al-Assad cast doubt on the Moscow initiative bearing any fruit.
Nevertheless, members of his government were expected to join the closed-door talks later in the week.
Moscow said more than 30 members of the Syrian opposition were taking part in the negotiations.
Russia's top diplomat Sergei Lavrov, who may also participate in the talks, said the aim of the first two days of discussion was to "provide a platform for the Syrian opposition so that they can develop some shared approaches to talks with the government."
"We plan that after two days of contacts between Syrians in Moscow, the representatives of the Syrian government will join the opposition, again just in order to establish personal contact," he said in televised remarks.
A Syrian government delegation headed by the ambassador to the United Nations, Bashar Jaafari, arrived in Moscow and was to join the talks on Wednesday, the Russian foreign ministry said.
Lavrov's deputy Mikhail Bodganov said Russia's top diplomat may meet with members of the opposition that day "if there is a constructive mood."
Russia says the Moscow meetings are part of a process aimed at restarting UN-mediated talks to end nearly four years of civil war that has claimed more than 200,000 lives since 2011.
Two previous rounds of talks in Geneva ended without success.
Russia, the most powerful backer of Assad's government, hopes to burnish its credentials as a diplomatic mediator while it is itself mired in a showdown with the West over the conflict in Ukraine.
Signup to our newsletter and follow us on Facebook and Twitter!
But the Syrian National Coalition said it was refusing to attend the talks in Russia given its status as Assad's top ally.
"Any talks should be held in a neutral country and overseen by the United Nations," a source in the coalition said in the run-up to the negotiations.
France's Foreign Minister Laurent Fabius said in Paris that a political solution to the crisis could not include Assad remaining in power.
"One needs a solution that involves both elements of the opposition and elements of the regime, not Assad," he said.
'Not every dialogue fruitful'
Even Assad appeared to pour cold water on the Russian initiative.
He told Foreign Affairs magazine in an interview published on Monday that some of the Syrian opposition members attending the talks are "puppets" paid by Qatar, Saudi Arabia or Western countries such as the United States, while others "don't represent anyone in Syria."
"You have to separate the national (opposition) and the puppets. Not every dialogue is fruitful."
Asked to comment on the chances of the talks succeeding, Assad said "optimism would be an exaggeration". But he added: "I would say we have hope, in every action."
In Syria, a government source earlier expressed hope that participants would agree on a roadmap to "fight terrorism", among other issues.
Washington has said it welcomed the Moscow talks but it was up to the opposition whether to attend.
The talks come amid signs that Washington may be recalibrating its Syria policy to focus more on the fight against the Islamic State jihadist group, which has taken control of parts of Iraq and Syria, rather than on toppling Assad.