"The enemies wanted to divide the people and to create a civil war, but the nation was alert," Khamenei said.
"If they were able to do it, the US and Zionist regime would have sent troops to Tehran's streets, but they knew it would hurt them. Thus they spread propaganda and supported the rioters."
Tehran has repeatedly blamed the US and its allies for fomenting the post-election unrest.
Ahmadinejad, in his own address marking Nowruz, vowed to defend Iran from foreign threats.
"Any unclean hand from any corner of the world that comes out from any sleeve and tries to harm the dear [Iranian] nation will be cut off with prudence, swiftness and steadfastness," he said.
The president also said that his government will continue to pursue a leadership role on the world stage.
Khamenei and Ahmadinejad's messages came after Barack Obama, the US president, addressed the Iranian peoplein a video broadcast on the internet.
In his message, the US president renewed his administration's offer of dialogue and criticised Tehran's leaders for "turning their backs" on previous overtures.
He also promised more educational and cultural exchanges, as well as support in ensuring that Iranians were able to get uncensored access to the internet.
Opposition protesters have used social media to organise their protesters and spread news and footage from demonstrations to the wider world.
Nowruz, a 12-day holiday, celebrates the arrival of spring and the beginning of the new year on the Persian calendar.