The United States issued the group's visas in two batches on Friday at its embassy in Berne, Switzerland.
Zarif said Manouchehr Mottaki, Iran's foreign minister, who had received his visa early on Friday, would take a commercial flight to New York to address the council.
US denial
Richard Grenell, a spokesman for the US mission to the United Nations, challenged Zarif's statement.
"Too late for what?" Grenell said. "The meeting hasn't even been scheduled yet. How can they say they are too late to come if the Security Council has not given a date and time for the event?"
In Berne, a spokesman for the US embassy said about 38 visas had been issued, including one for Ahmadinejad, early on Friday, and another 40 had been processed for the rest of the group late in the day once all the paper work had been completed.
"The applications were incomplete but they were completed this morning," Daniel Wendell, press attache at the embassy, said. "The two batches amount to about 75 visas ... that's a pretty sizeable group."
Ahmadinejad had said he wanted to attend the Security Council meeting at which a vote is expected on Saturday on a new resolution strengthening UN sanctions against Iran.
The new draft, which toughens sanctions imposed in December in response to Tehran's continued refusal to halt sensitive nuclear work, was presented last week to the council's 10 non-permanent members for their comments.
The sanctions package is contained in the draft by the council's five members with a veto – Britain, China, France, Russia and the US – plus Germany.