Mr Annan's 10-day tour of the Middle East has been mainly aimed at implementing the UN resolution which halted a 34-day conflict that killed more than 1,200 people in Lebanon, overwhelmingly civilians, and 160 Israelis, mostly soldiers.
Mr Annan said after talks with the president that Mr Ahmadinejad assured him Tehran would support the implementation of the UN resolution that ended the fighting in Lebanon and was ready to negotiate over its nuclear program.
State radio quoted Mr Ahmadinejad as saying that "Iran is ready to help in the reconstruction of Lebanon and seriously take part in any group activity to rebuild Lebanon."
He also said that Israel and its allies Britain and the United States "should compensate Lebanon for the damage inflicted".
Meanwhile Mr Ahmadinejad told Mr Annan at the Tehran meeting that he was prepared to negotiate on Iran's nuclear program but would not accept a suspension of uranium enrichment before talks, rejecting a key demand of Western countries.
"The president assured me ... Iran is prepared to negotiate and find a way out of this crisis," Mr Annan said.
But he added that Mr Ahmadinejad had also said that "Iran does not accept a suspension (of uranium enrichment) before negotiations".
Mr Annan expressed hope that the Islamic republic and the international community would find a way to move forward at talks between EU foreign policy chief Javier Solana and Iran's lead nuclear negotiator Ali Larijani this week.
Iran has defied Western demands to suspend uranium enrichment and rejected a UN deadline that has left it facing a push by the United States for the Security Council to impose sanctions.
No ‘legal basis’
Iran’s ambassador to the International Atomic Energy Agency said that neither the UN Security Council nor international treaties can legally require Iran to stop enriching uranium.
"We do not see any legal basis for this demand," Ali Asghar Soltanieh told CNN television.
"There is no limitation or restriction" on peaceful uses of nuclear power in International Atomic Energy Agency or nuclear Non Proliferation Treaty rules, he told CNN's "Late Edition."
"There is no provision in the IAEA statute also and NPT (Nuclear Non-proliferation Treaty) for requesting a country to stop or suspend enrichment activities," the ambassador to the IAEA said from Vienna.
"The only thing is that the IAEA has to verify and control the activities to make sure that there is no diversion" of fissile material to use in weapons.
He called the most recent report by IAEA chief Mohamed ElBaradei "a document proving our assertion that all activities have been for peaceful purposes and there is no evidence of diversion to nuclear material."
The United States accuses Iran of seeking nuclear weapons, a charge fiercely denied by Tehran, which insists that its nuclear program is solely aimed at providing civilian energy.