He also welcomed Syria's acceptance of the Chemical Weapons Convention and condemned the use of such weapons.
Earlier, US President Barack Obama said he was encouraged by Mr Rouhani's "more moderate course"
He told the General Assembly that the diplomatic approach to settling the dispute over Iran's nuclear programme must be tested.
Mr Rouhani, who was elected earlier this year, has pledged a more open approach in international affairs.
Iran is under UN and Western sanctions over its controversial nuclear programme.
Tehran says it is enriching uranium for peaceful purposes but the US and its allies, including Israel, suspect Iran's leaders of trying to build a nuclear weapon.
'Full transparency'
President Rouhani said the "so-called Iranian threat" was imaginary.
"Iran poses absolutely no threat to the world or the region," he said.
"Nuclear weapon and other weapons of mass destruction have no place in Iran's security and defence doctrine, and contradict our fundamental religious and ethical convictions. Our national interests make it imperative that we remove any and all reasonable concerns about Iran's peaceful nuclear programme."
To this end he said Tehran was prepared to engage "immediately in time-bound and result-oriented talks to build mutual confidence and removal of mutual uncertainties with full transparency".
He criticised the use of international sanctions against Iran, comparing them to the punitive measures used against Iraq while Saddam Hussein was in power.
"These sanctions are violent - pure and simple," he said, adding that it was not political elites that were affected "but rather... the common people".
President Rouhani said that, while condemning any use of chemical weapons "we welcome Syria's acceptance of the Chemical Weapons Convention".
Iran, a staunch ally of Syria, has criticised US threats of military strikes over the deadly chemical weapons attack on 21 August in the suburbs of Damascus.
Speech 'cynical'
Syria has since agreed to a joint US-Russian plan to have its chemical weapons arsenal destroyed.
President Rouhani said Tehran believed that access by extremist groups to chemical weapons "is the greatest danger to the region".
He added: "Simultaneously, I should underline that illegitimate and ineffective threat to use or the actual use of force will only lead to further exacerbation of violence and crisis in the region."
However, President Rouhani's address failed to impress Israeli Prime Minister Benjamin Netanyahu who described it as "cynical... full of hypocrisy".
"It had no practical suggestion to stop Iran's military nuclear programme and no commitment to fulfil UN Security Council decisions," he said in a statement.
In his speech, Mr Obama called for a strong UN resolution on Syria's chemical arms....
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