Zhenmin said negotiators were aiming for a vote this week, "but it seems that this week is not possible".
Jean-Marc de la Sabliere, France's UN ambassador, said he hoped for an early vote.
"There is a lot of support for the text in the council, but as I have said, we would like to have if possible a consensus," he said.
Mahmoud Ahmadinejad, Iran's president, has made plans to speak to the council on the day of the vote.
"I'm not gutting the resolution. I'm improving it"
Dumisani Kumalo, South Africa's ambassador to the UN
The UN resolution can be adopted without Pretoria's consent, but the big powers would like a unanimous vote and no abstentions from an influential country such as South Africa.
South Africa favours restricting the sanctions to nuclear-related programmes only, although its proposals call for a 90-day "time-out" on all penalties.
It presented a list of amendments that would delete nearly all the new resolution's main provisions, including an embargo on conventional arms that Iran can export and most of the list of people and institutions whose financial assets abroad would be frozen.
Dumisani Kumalo, Pretoria's UN ambassador, said he would explain to the Security Council members later on Wednesday the purpose of his proposals.
"I'm not gutting the resolution. I'm improving it," Kumalo said.
The new UN resolution is a follow-up to one adopted in December banning trade in sensitive nuclear materials and ballistic missiles as well as freezing assets of individuals and institutions associated with atomic programmes.
The US and leading Europeans say Iran is trying to develop a nuclear bomb under the guise of a civilian nuclear programme. Tehran says its programme is for power generation.
Russia, which was instrumental in drafting the resolution, is building a light-water reactor at Bushehr in southern Iran.
Moscow denies it had told Tehran that it would not deliver fuel if Iran did not meet Security Council demands to suspend uranium enrichment, which can be used to make bombs.