The Syrian government and the opposition took part in four days of indirect talks aimed at ending the war.
Staffan de Mistura told the Security Council that "important gaps remain between the parties on major issues" following the sixth round in Geneva held last week.
The Syrian government and the opposition took part in four days of indirect talks aimed at ending the war that has killed more than 320,000 people since 2011.
De Mistura said all sides were ready to return to the table for a new round of talks "which we intend to target sometime in June."
The envoy said the talks are to lay the groundwork for "a real negotiation" and expressed hope that this "will be possible before too long."
Hopes for a breakthrough in the near future remain dim, with the fate of President Bashar al-Assad still a major stumbling block.
The opposition insists that Assad must leave power as part of any peace deal but the government has rejected the demand.
A series of expert-level talks will take place to pursue discussion on a range of issues including the thorny matter of a new constitution, but the UN envoy stressed that these would not be decision-making meetings.
"We are not seeking to draft a new Syrian constitution in Geneva," said De Mistura. "We are laying foundations for the time when the Syrians can do that."
Following closed-door Security Council talks, Uruguay's Ambassador Elbio Rosselli, who holds the council presidency, said there were concerns about the slow pace of the peace process.
"The members obviously have concerns on the slow movement, but at the same time, (are) somewhat pleased in having moved a little bit forward," Rosselli told reporters.
The council is also weighing whether to back a deal reached between Russia, Iran and Turkey to set up de-escalation zones in Syria where a ceasefire would be buttressed with a ban on flights and where aid deliveries would be ensured.
France said it would not support the deal reached in the Kazakh capital of Astana on May 4 unless it has strong international monitoring and would allow for sanctions in case of violations.
"This is a key requirement from France," said Ambassador Francois Delattre.
Britain also said monitoring was key and that there should be reports to the Security Council on implementation of the Astana deal.