Annan was speaking after talks in Iran with the Iranian president.
At the same time, Annan said Ahmadinejad once again rejected any suspension of Iran's uranium-enrichment program before negotiations.
Iran's rejection of that demand, contained in the latest Security Council resolution, could make it subject to sanctions.
Annan also said Ahmadinejad promised Tehran's full support for the cease-fire resolution in Lebanon between Israel and Hizballah, an ally of Iran.
Annan had on September 2 met with Iran's top nuclear negotiator, Ali Larijani, who described the talks as "constructive" and said "both sides agreed that problems should be solved through negotiations."
Annan's talks in Tehran ended hours before Larijani was due to meet the EU's foreign affairs chief, Javier Solana.
On September 2, Solana said the talks with Iran are not negotiations, but clarifications of the Iranian position.
EU foreign ministers have expressed a desire for renewed diplomacy, but said they would not give Iran much time to resolve its standoff with the international community.
Iranian Foreign Ministry spokesman Hamid Reza Assefi said on September 3 that Iran expects the EU to take a stand "in the coming days" on Tehran's response to the package of incentives offered to Iran in a bid to persuade it to suspend its enrichment program.
(compiled from agency reports)
Afraid Of Sanctions?
WHAT DOES TEHRAN REALLY THINK? On August 22, Radio Farda correspondent Fatemeh Aman spoke with Alex Vatanka, Eurasia editor for Jane's Information Group, by telephone from Alexandria, Virginia. Vatanka discussed the possible impact that comprehensive sanctions could have for Iran.
Radio Farda: Some Iranian authorities are trying to create the impression that they aren't concerned about the possibility of international sanctions against it. They emphasize that what Iran has achieved so far has happened despite the sanctions already in place against it. Are they really not afraid of sanctions?
Vatanka: I think that what the Iranians are trying to do is to continue to play this balancing act. On the one hand, they are trying to say, "Look, we have done without you for 27 years; we can continue." On the other hand, if you look at every other major Iranian overture toward the U.S., obviously what they are hoping to do is remove those sanctions. It is the sanctions that have been the biggest obstacle to a genuine expansion in the Iranian economy. It is the sanctions and U.S. policies vis-a-vis Iran that have, for instance, kept Iran from joining the World Bank. It is sanctions and so on that have made the Iranian oil industry have such a tough time in bringing investment into the strategic oil and gas sectors. People like [former Iranian President Ali Akbar Hashemi-]Rafsanjani back in the mid 1990s even kept certain fields untouched because the idea was that U.S. companies should have those once the sanctions were lifted.
I think sanctions are quite important to the Iranians, but at the same time what they are trying to say is, "Don't assume that we are going to fall off our chair just because you mentioned the sanctions card." It is part of a kind diplomatic chess game going on by Tehran. But remember if we look and listen to Iranian reformists, this is being openly debated inside Iran. The question that is being asked of [President Mahmud Ahmadinejad and his entourage] is, "What is the ultimate objective?" Is it just Islamic independence? Is it just the ability to enrich uranium? The debate in Iran by the reformists -- and I think a lot of people would sympathize with this -- is, "What are we being sanctioned for exactly and what policies do you have to make sure that those sanctions don't hit us harder than we have already been hit?"
Remember, the big issue here is this: Iran has been sanctioned by the U.S. Iran has never faced comprehensive United Nations sanctions. The Iranian people have never suffered on a scale that the Iraqi people, for instance, suffered because of such sanctions. So it is kind of disingenuous of these senior leaders to pretend that Iran has already gone through comprehensive sanctions. Iran has not. And it will be totally different set of circumstances that will have a totally different impact on Iranian society and the economy, should the UN impose comprehensive sanctions on the country.
THE COMPLETE PICTURE: RFE/RL's complete coverage of controversy surrounding Iran's nuclear program.