As the talks kicked off in Moscow, fighting raged in Syria's second city of Aleppo, with state media reporting that rebel fire on a hospital killed three women.
Another 11 people were killed in rebel attacks on other government-held neighbourhoods, Sana state news agency said.
In televised remarks, de Mistura praised the two-month-old truce brokered by Moscow and Washington as a "remarkable achievement" and said the two global powers should help "all of us to make sure that this is brought back on track".
Russia's top diplomat for his part said that "there was no alternative to the political settlement of the Syrian crisis," adding Moscow highly valued Mistura's efforts to help negotiate an end to a conflict that has killed more than 270,000 people since 2011.
"I am looking forward to a fruitful discussion," Lavrov added.
The talks in the Russian capital were a last-ditch bid to rescue peace negotiations that have been undermined by the fierce fighting around Aleppo.
The meeting comes after a day of diplomacy in Geneva, where US Secretary of State John Kerry added his weight to efforts to resuscitate the stuttering truce.
