"We welcome change but on condition that change is fundamental and on the right track," Ahmadinejad said.
"When they say 'we want to make changes', change can happen in two ways. First is a fundamental and effective change ... The second ... is a change of tactics.
"It is very clear that, if the meaning of change is the second one, this will soon be revealed."
Continuing on the theme of "change", Ahmadinejad said: "Those who say they want to make change, this is the change they should make: they should apologise to the Iranian nation and try to make up for their dark background and the crimes they have committed against the Iranian nation."
Apology demanded
The remarks by Ahmadinejad come after Obama called on Tehran to "unclench its fist" so that a positive relationship with Washington can begin.
The new US administration has said Obama would break from his predecessor by pursuing direct talks with Tehran.
However, it has also made clear that Iran will face increased pressure if it does not observe demands by the UN Security Council to halt sensitive nuclear work.
While Washington and its Western allies say that Iran is trying to make a nuclear weapons, Tehran says it is only trying to generate electricity and has refused to stop its uranium enrichment work.
Withdrawal call
Ahmadinejad also accused Washington of trying to stifle Iran's economic development since the 1979 Islamic revolution.
"Who has asked them [the United States] to come and interfere in the affairs of nations?" he said, while calling on the US to withdraw its troops from the Middle East.
Washington has accused Iran of sponsoring groups such as Palestinian Hamas and the Lebanese Hezbollah movement, which are both on the US list of "terrorist" organisations.
Hillary Clinton, the US secretary of state, has signalled that Washington is ready to talk to Tehran, saying that the Iranian government has a "clear opportunity" to show its face to the West.