Beijing agreed in late March to discuss possible sanctions, paving the way for the meeting to go ahead.
Earlier on Thursday, Dmitry Medvedev, the Russian president, said Iran’s nuclear activity could not be ignored.
“We cannot turn a blind eye to this,” he said, adding that Russia favoured “smart” sanctions.
The envoys from the six countries are expected to discuss the details of a possible resolution, which diplomats have said will target Iran’s Revolutionary Guard and toughen existing measures against the country’s shipping and banking sectors, as well as singlin out companies connected to the nuclear programme.
There are currently three UN resolutions mandating sanctions against Iran. They were agreed in advance by officials from the six countries before being passed to UN ambassadors to finalise.
In contrast these negotiations have begun at ambassadorial level in an effort to obtain a quick resolution, after Barack Obama, the US president, called for the security council to act within weeks.
Speaking on Thursday, Rice reiterated that Washington wants to see a resolution agreed in the near future. “We’re working to get this done swiftly,” she said.