Staffan de Mistura told a closed session of the council that more progress was needed to strengthen a ceasefire and deliver humanitarian aid before talks can resume, according to diplomats in attendance.
Two weeks of UN-brokered talks between the Syrian government and opposition groups in Geneva ended on April 27 with no breakthrough.
There had been expectations that a new round would be called at the end of May, but fighting has flared on the ground and aid deliveries to besieged areas continue to be blocked.
The 20-nation group backing the Syrian peace process has said that it is up to De Mistura to decide on the appropriate time to resume the talks.
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The envoy has repeatedly called on the United States and Russia to take action to shore up the ceasefire that has been in place since February 27.
There have been appeals to Russia, Syria's ally, and other players to put pressure on all warring factions to allow aid deliveries to reach civilians.
There "are plenty of civilians at the moment in danger of starvation," he told reporters in Geneva.
The peace talks are to reach a settlement to end the five-year war that has left 280,000 dead and driven millions from their homes.