Bush to a live television debate two days ahead of a UN deadline for Iran to halt its controversial nuclear program.
"I suggest we talk with Mr Bush, the president of the United States, in a live television debate about world issues and ways out of these standoffs. We would voice our opinions and they would too," he told a news conference.
The debate "should be uncensored, above all for the American public", said Mr Ahmadinejad. Earlier this year he sent Mr Bush a letter in the first contact in decades between leaders of the two arch-foes.
However a White House official rejected the debate offer outright, dismissing Mr Ahmadinejad's move as "just a diversion from the legitimate concerns that the international community, not just the US, has about Iran's behaviour".
Mr Ahmadinejad said Iran would be prepared to restore ties frozen by the United States after the seizure of the US embassy in Tehran in 1979.
But Washington would first have to change its tone towards the Islamic republic.
"We would like to have relations with all countries except for the one country which we see as illegitimate and imposed," he said, referring to Israel which Tehran refuses to recognise.
"The US is not an exception, but United States cut the ties to pressure us. The US administration is still dreaming about returning the Iranian nation to 30 years back.
"They have to wake up from this dream, correct their behaviour and language, take a fair stance. They cut the ties, they should provide the conditions themselves," he said.
Foreign ministers meet
Later, Chinese Foreign Minister Li Zhaoxing met with Iranian Deputy Foreign Minister Abbas Araghchi Wednesday to discuss the Iranian nuclear issue, the Chinese government said.
"The two sides mainly exchanged views on developments in the Iranian nuclear issue," the Chinese foreign ministry said in a statement posted on its website, following the meeting in Beijing.
"They emphasised the issue should be appropriately resolved through negotiations," the statement added.
China last week urged the Islamic republic to be constructive in its dealings on the issue.
UN deadline
The clock continued to tick down to a Thursday deadline from the UN Security Council for Iran to suspend all uranium enrichment and reprocessing activities.
The Vienna-based International Atomic Energy Agency (IAEA) will report to the Security Council the same day on Iran's compliance with its demands.
Iran has insisted it has no intention of abandoning such work and faces possible sanctions if it fails to comply.
But Mr Ahmadinejad said he believed it was "unlikely" the Security Council would act against Iran over its nuclear programme, which the US maintains is cover for a weapons drive.
"We have said everything in our response. I think the time to use the instrument of the Security Council has expired," he said.
He was referring to Iran's answer to a Western package of incentives over its nuclear program, which Iran says is for civilian energy purposes only.
"I see it as unlikely that they want to use it (the Security Council). Using nuclear energy is Iran's right and we want to use it according to international law," Mr Ahmadinejad said.
British ambassador to the United Nations Emyr Jones Parry said he expected the Security Council to wait a couple of weeks before discussing what action to take.