Staffan de Mistura told a closed session of the Security Council on Thursday that more progress was needed to strengthen a ceasefire and deliver humanitarian aid before talks can resume.
The envoy "briefed on his intention to start the next round of talks as soon as feasible but certainly not within the next two/three weeks," said a statement from his office.
Two weeks of UN-brokered talks between the Syrian government and opposition groups in Geneva ended on April 27 with no breakthrough.
A new round had been expected for the end of May, but no new date has been announced.
Diplomats said there was little chance that the opposition would take part in a new round of peace talks if violence was raging and no aid was reaching civilians.
De Mistura "reiterated the need to see progress on the ground -- particularly in reference to the cessation of hostilities and humanitarian access," said the statement.
The envoy has called on the United States, which backs moderate opposition groups, and Russia, the Syrian leader Basha al-Assad’s ally, to take action to shore up the ceasefire that has been in place since February 27.
US Ambassador Samantha Power told reporters that the violence on the ground had reached "pre-cessation-of-hostilities levels" and blamed the Damascus regime for the upsurge in fighting.
"The dangers to the cessation are largely being driven by the Syrian regime and its allies," Power said.
"Russia has special responsibility to press the Assad government to abide by the cessation of hostilities and end its bombardment and siege of innocent civilians," she added.
De Mistura earlier told reporters in Geneva that many Syrians will face starvation if the regime and rebel groups do not allow greater access to humanitarian convoys.
There "are plenty of civilians at the moment in danger of starvation," he said.
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. — AFP