Dumisani Kumalo, South African UN ambassador and president of the Security Council for March, said he had received a letter from his Iranian counterpart, Javad Zarif, requesting the council visit by Ahmadinejad.
The move by the five permanent members of the council and Germany, which may be adopted next week, would penalise Tehran for refusing to suspend uranium enrichment.
The major-power agreement includes a ban on Iranian arms exports, an assets freeze on individuals and firms involved in Tehran's nuclear and ballistic missile programmes and a call to nations and institutions to bar new grants or loans.
"It is stubbornness and pride on Iran's part that has led to this impasse, and it can only lead to disaster for Iran"
Diom1982, Cork, Ireland
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"We have confirmed we have an agreement on the text," Emyr Jones Parry, Britain's UN ambassador, announced after consultations with his counterparts.
"The United Kingdom will introduce that text," he said.
Alejandro Wolff, a US ambassador, told reporters: "I'm satisfied with the compromise outcome," which was sent to governments of the six countries on Wednesday night.
"There are lots of things that we would have wanted handled differently," he said. "I think that's a fair statement that would apply to every member."
The new measures follow a resolution adopted in December that imposed trade sanctions on Iran's sensitive nuclear materials and technology, and froze the assets of some Iranian individuals and companies.
Iran, which says its nuclear programme is for peaceful uses only, ignored a February 21 deadline to suspend enrichment or face further action.
A key element is a new list of individuals and entities subject to financial sanctions, such as firms owned by Iran's Revolutionary Guards and the state-owned Bank Sepah.
The text says Iran is banned from exporting any conventional weapons. But the measure calls on states to "exercise vigilance and restraint" in shipping any heavy weapons to Tehran.
The measure would suspend the sanctions if Iran complies with the council's demands within 60 days. If Tehran does not, further action would be considered.