In his first major international speech since becoming president in June, Ahmadinejad on Wednesday advanced broad concepts, including a recommendation that the UN "institutionalise justice at the international level".
He made no new proposal to resolve a dispute with the US and Europe over Iran's nuclear ambitions, but was due to address the UN General Assembly again on Saturday.
Ahmadinejad was not shy about taking on the US, which hosts the world body at its headquarters in New York and has accused Iran of pursuing nuclear weapons in contravention of international commitments.
"Greater power or wealth should not accord expanded rights to any (UN) member," he said in a speech to a UN summit, adding: "The host country should not enjoy any right or privilege over the rest of the memberships."
"The host country should not enjoy any right or privilege over the rest of the memberships"
He also criticised "unilateralism, production and use of WMD (weapons of mass destruction), intimidation, resort to the threat or use of force and imposition of destructive wars on peoples for the sake of security and prosperity of a few powers".
Ahmadinejad, who was mayor of Tehran until his election, told other leaders: "The greatest challenge of our age is the gradual spritiual depravation of human beings brought about by the distancing of the prevailing order from morality and unity of monotheism."
"The United Nations should lead in the promotion of spirituality and compassion for humanity," he added.
Several thousand Iranian exiles meanwhile protested in front of the UN headquarters during the day, denouncing Ahmadinejad as a "terrorist".
"Iranians think Ahmadinejad is not their representative, he's a
terrorist," said Bahman Badiee of the Iran Society of South
Many Iranian exiles condemned
Ahmadinejad's visit to the UN
The vast majority of demonstrators were members of the National Council of Resistance in Iran (NCRI), whose president Maryam Rajavi lives in exile in France.
The NCRI is the political arm of the People's Mujahedeen (MEK), which has been fighting the Islamic government in Tehran since the mid-1980s.
The MEK has been branded a terrorist organisation in both the
US and EU, and Rajavi is leading the campaign to have the label removed.
The protesters carried banners reading "No to terrorist
Ahmadinejad" and "Terrorist Ahmadinejad - Out of UN".