"On the Iranian issue, there has been talk for quite a while that the issue may be brought to the Security Council," Annan told reporters.
"It hasn't been, and I am not expecting it to come to the Security Council in the foreseeable future.
"I have also encouraged those who would want to bring it to the Security Council to do as much as they can to resolve it, or if they are going to bring it to the Security Council, they must have very clear ideas on what action they expect the council to take, because it would be easy to dump it on the council without any real expectation as to how the council will handle that."
The International Atomic Energy Agency (IAEA) is investigating Iran's civilian nuclear program for evidence it is being used to build a nuclear weapon in violation of its obligations under the Nuclear Non-Proliferation Treaty.
In the event such evidence is found, the IAEA, the UN's nuclear watchdog, could ask the Security Council to impose sanctions.
The United States has on several occasions in the past two years said it was time for the IAEA to refer the Iranian nuclear question to the security council.
But the State Department said Thursday it has not asked for the council to consider the Iran nuclear case.
"The United States has felt that it's important for the IAEA to continue its pressure on Iran, to continue its investigation, its inspections, to continue finding things out about this program," department spokesman Richard Boucher said.
"And as they have continued to do that, including in recent days, including by this revelation that we had in recent days, we think it's appropriate for the board to continue the activity that's going on now," he added.