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".
"I am looking forward to a fruitful discussion," Lavrov added.
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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.
Rebel rocket fire on other government-held neighbourhoods killed another 11 people, it added.