His comments, in a speech marking the 34th anniversary of the Islamic revolution that ousted the US-backed shah in 1979, came just days after Iran's supreme leader rejected US Vice President Joe Biden's call for direct talks.
They also come at a time when Tehran and six world powers are preparing to resume stalled talks over Iran's nuclear programme in the Kazakh city of Almaty on February 26.
"The change of tone is necessary but not sufficient," Ahmadinejad said at Tehran's landmark Azadi (Freedom) Square amid chants of "Death to America."
"Stop pointing weapons at the Iranian nation and I will myself negotiate with you," he said, addressing the United States directly.
"Talks should be with respect, fairness and not under pressure."
"You have done everything to prevent us from becoming nuclear and you have failed. The best solution is cooperation and understanding."
Last week Biden made a "serious offer" for direct talks in the framework of negotiations between Iran and the so-called P5+1 (the United States, France, Britain, Russia, China and Germany) on Tehran's nuclear programme which world powers suspect is aimed at making atomic weapons.
Iran vehemently denies the allegation.
Supreme leader Ayatollah Ali Khamenei, who has the final say on all national issues, rejected Biden's offer outright.
"I am not a diplomat but a revolutionary and I speak frankly," Khamenei was quoted as saying on his website on Thursday. "You (Americans) are pointing the gun at Iran and say either negotiate or we will shoot."
On Sunday, Ahmadinejad called on Iranians to remain "united behind" Khamenei, reiterating that "the Iranian nation will not give up an inch of its legitimate rights."
Tehran is currently under a series of international and Western sanctions aimed at curbing its nuclear ambitions, mainly the sensitive process of uranium enrichment.
The punitive economic measures have led to a severe economic crisis, choking Iran's banking system and limiting oil exports, its main foreign revenue earner.
A banner at Azadi Square on Sunday tried to give a different picture, declaring: "The crippling sanctions have only tickled us."
A recent survey by US polling firm Gallup said that Iran's nuclear programme is supported by a large majority of its population.
Hundreds of thousands of Iranians, chanting anti-US and anti-Israel slogans, marked the anniversary of the Islamic Revolution on Sunday.
Waving Iranian flags and portraits of Islamic republic founder Ayatollah Ruhollah Khomeini and of Khamenei, crowds gathered at Azadi Square in a government-sponsored rally which has become a regime cornerstone.
The authorities put on display a replica of a rocket which Iran says was used to carry a monkey into space in late January.
Sunday's nationwide rallies mark February 11, 1979 when the then Iranian army declared solidarity with the people, turning its back on Shah Mohammad Reza Pahlavi.
Ten days beforehand, Khomeini had returned in triumph from exile in France to lead the revolutionaries to power.