"Today is a day when we have to forget all our rivalries and turn them into friendships," Ahmadinejad said on Saturday in comments broadcast on state radio - his first since being declared winner of Friday's election.
"We are one nation and one big family. We should help each other to make a great society," he added.
Official election results showed that the Tehran mayor comfortably defeated experienced political heavyweight Akbar Hashemi Rafsanjani, securing some 62% of the ballots cast.
Analysts say Ahmadinejad, 48, earned the support of the urban and rural poor. Rafsanjani, 70, in contrast, drew heavy support from wealthy Iranians, fearful that Ahmadinejad would enforce strict moral codes and further isolate the country from the West.
"I am certainly proud to be elected by the Iranian people. But more than that, I am proud to be able to work for Iran, now at the municipality and as president in the future," he said.
"I feel the heavy weight of responsibilities on my shoulders"
Ahmadinejad will take up office in August. "I feel the heavy weight of responsibilities on my shoulders," he added.
Khamenei chides US
Meanwhile, Iran's supreme leader Ayat Allah Ali Khamenei has said the United States has been "humiliated deep inside" by the republic's presidential election.
"You illustrated the secret of your solidity and power against the expansionist policies of the arrogance of the world," Khamenei said in a message to the Iranian people, read out on state television on Saturday.
"Despite its babbling, your enemy is now humiliated," he told Iranians. He said the election was "practical proof of your commitment to bravely guard the Islamic republic's interests (and) fulfil all the Islamic and revolutionary ideals".
He congratulated president-elect Ahmadinejad, urging "his and the other candidates' supporters to show capacity, patience and wisdom". He also offered greetings to Rafsanjani.
"I deeply appreciate all the other candidates, especially Hojatoleslam Hashemi Rafsanjani, who is for the Islamic system like always," Khamenei said.