"But the way to do that is not by Iran forgetting the previous hostile and aggressive attitude of the United States.
"The American administration has to recognise its past mistakes and repair them as a way to put away the differences."
The US is at odds with Iran over its nuclear programme, which Washington says is aimed at building atomic weapons, while Tehran insists it is for the peaceful generation of electricity.
The US is also concerned over Iran's missile-development efforts.
The US cut off diplomatic ties with Iran during the 1979-1981 hostage crisis, in which a group of Iranian students held 52 US diplomats hostage at the American embassy for 444 days.
Iran's leaders did not mention Obama's speech in speeches given to mark the Nowruz celebrations on Friday.
But Ayatollah Ali Khamenei, Iran's supreme leader, said that tests at the Bushehr nuclear plant in the south of the country had convinced other nations that its nuclear plans would not be abandoned.
"This is the results of the progress of our scientists ... which persuaded the whole world that the path of Iran's nuclear progress could not be blocked," he said.
With Friday's appeal, Obama went further than he has since taking office on January 20 in extending an olive branch to Tehran.
"My administration is now committed to diplomacy that addresses the full range of issues before us, and to pursuing constructive ties," he said in the message.
The White House distributed the videotape and posted it on its website on Friday to coincide with Nowruz, a festival celebrating the arrival of spring.
His administration earlier expressed an openness to face-to-face diplomatic contacts with Tehran.
It marks a major shift from the policy pursued by the administration of George Bush, Obama's predecessor, towards Iran, which he once branded as part of an "axis of evil".
Al Jazeera's Alireza Ronaghi, reporting from Tehran, said Iranians have taken a wait-and-see approach to changes in US policy after Obama took office.
"Now they see for the first time in many years Iran being addressed as the Islamic Republic of Iran. It is a point of recognition for Iran," Ronaghi said.
|Obama's said US wants Iran to take its rightful place in the community of nations [Reuters]
"An opportunity has been given to the current administration [of] President Ahmadinejad, to solve outstanding issues that no other government in Iran has been able to address. He is not going to miss this opportunity."
In his video appeal on Friday, Obama said the US wanted Iran to take its "rightful place in the community of nations".
"This process will not be advanced by threats," he said. "We seek instead engagement that is honest and grounded in mutual respect."
But Obama also insisted that Tehran do its part to achieve reconciliation.
"You have that right - but it comes with real responsibilities, and that place cannot be reached through terror or arms, but rather through peaceful actions that demonstrate the true greatness of the Iranian people and civilisation," he said.
"The measure of that greatness is not the capacity to destroy, it is your demonstrated ability to build and create."