"Iran is in non-compliance with mandatory obligations imposed by the Security Council.
"We think it would be perverse in response to that situation to say, 'Oh, by the way, we now lift the obligations which currently apply to Iran'."
South Africa has said the draft resolution - which would freeze the assets of some senior Iranian military leaders and of the state-owned Bank Sapeh - should be changed because its provisions went beyond Iran's nuclear programme.
"I told them we are making the amendments in the spirit of adding value to the draft," Dumisani Kumalo, South Africa's UN ambassador and the current council president, said after Wednesday's meeting.
Kumalo also said he doubted the resolution would now be passed this week because any changes would need the approval of 15 different governments.
But France's UN ambassador, Jean-Marc de la Sabliere, said: "Our wish is to have the resolution by the end of the week."
Earlier on Wednesday Mahmoud Ahmadinejad, the Iranian president, had denounced "Zionists who dominate the world" in a message marking the Iranian new year, or Nowruz, and said Iran was determined to defend its position in the nuclear standoff.
Ayatollah Ali Khamenei, Iran's supreme leader, also warned foreign powers not to threaten his country.
"If they want to threaten us and use force and violence against us, they should not doubt that Iranian officials will use all they have in their power to deal a blow to those who assault them," he said in a televised speech.
Iran has said that its nuclear programme is intended to generate electricity, but the US and some European nations have said Tehran wants to build a nuclear weapon.
South Africa dismantled its nuclear weapons programme in the early 1990s during its transition from white-minority rule, and has consistently defended Iran's right to enrich uranium for peaceful purposes.