"We welcome the wish of the president of the United States to put away past differences," Ali Akbar Javanfekr told the AFP news agency.
"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."
Javier Solana, the EU's foreign policy chief, voiced hope that the video message could open a "new chapter in relations with Tehran."
"I hope very much that the Iranians will take good attention of what has been said by President Obama," he said.
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.
With Thursday's appeal, Obama went further than he has since taking office on January 20 in extending an olive branch to Tehran.
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".
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.
'Point of recognition'
Al Jazeera's Alireza Ronaghi in Tehran said: "Iranians have always said they have to wait and see what exactly the changes are [between Bush and Obama].
"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.
|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, [under] 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, Obama said: "This process will not be advanced by threats. We seek instead engagement that is honest and grounded in mutual respect."
He said the US wanted Iran to take its "rightful place in the community of nations", but 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."
Obama said "he is seeking "a future with renewed exchanges among our people and greater opportunities for partnership and commerce".
However, he acknowledged that "this won't be reached easily".
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.