The talks are the first since two rounds of negotiations collapsed in 2014.
Syria's conflict has killed more than 250,000 people, displaced millions and sent hundreds of thousands as refugees to Europe.
The first meeting was between the UN Special Envoy to Syria Staffan de Mistura and a government delegation headed by the country's ambassador to the UN, Bashar Ja'afari.
A UN spokesman said that he would later meet with other delegates, including civil society representatives.
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The meetings are part of a process outlined in a UN resolution last month that envisages an 18-month timetable for a political transition in Syria, including the drafting of a new constitution and elections.
The opposition boycott is a blow to the UN's attempt to bring representatives of President Bashar Assad's government and his opponents together for talks on ending the conflict.
On the eve of the talks, de Mistura appealed to Syrians to make concessions and described the talks as "an opportunity not to be missed."
Earlier today UN spokesman Ahmad Fawzi reflected the sense of chaos and confusion surrounding the beginning of peace negotiations when he told reporters at a briefing that "I don't have a time, I don't have the exact location, and I can't tell you anything about the delegation."
Ahmad Ramadan, a senior official with the Syrian National Coalition, which is part of the HNC, said the opposition will boycott the talks until it receives assurances on the implementation of UN Security Council resolutions on lifting the sieges and halting bombardment of civilians in Syria.
"There cannot be any negotiations as long as the humanitarian issues have not been discussed or implemented," he said.