The council last year adopted three rounds of tough economic sanctions on North Korea, banning most of its exports of raw commodities and severely restricting oil supplies.
Asked about lifting sanctions, Russian Ambassador Vassily Nebenzia told reporters: "I think that it is only natural that we should be thinking about steps in that direction."
"There is progress on the track that should be reciprocal. There should be a two-way street," he said. "Of course the other side should see encouragement to go forward."
At the first-ever meeting between sitting leaders of the US and North Korea yesterday in Singapore, President Donald Trump and Kim Jong Un pledged in a joint statement to work toward the "complete denuclearisation of the Korean Peninsula."
The United States along with Japan and European countries maintain that the raft of tough sanctions must remain in place until North Korea has fully dismantled its weapons programmes.
The council is expected to meet to discuss the results of the Singapore summit, but Nebenzia, who holds the council presidency this month, said nothing had been scheduled yet.
"It would be interesting to hear from those who were directly involved their assessment of the results," said the Russian ambassador.
Many diplomats credit the UN move to ramp up sanctions as a decisive factor in pressuring Kim to agree to negotiate an end to North Korea's military programme.
Dutch Ambassador Karel van Oosterom, who heads the council's sanctions committee on North Korea said the punitive measures were still being applied in full force.
"We will continue to keep up the pressure with the full implementation of the sanctions," he said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)