The president devoted a significant proportion of his speech to the challenges of finding a peaceful settlement in the Middle East - and called for the relaunch of "negotiations without preconditions".
The BBC's diplomatic correspondent, Jonathan Marcus, says Mr Obama used his first speech to the General Assembly to signal that the United States was back as a team player on the international stage.
His speech received warm but not effusive applause, a sign perhaps that in the face of real world problems the expectations surrounding the president are gradually being adjusted to reality, our correspondent says.
In other contributions to the General Assembly:
UK Prime Minister Gordon Brown said he was looking into reducing the UK's fleet of nuclear weapon submarines from four to three, as part of a "grand global bargain" he proposed between nuclear and non-nuclear states to combat nuclear proliferation
Mr Sarkozy told Iranian leaders they were "making a tragic mistake" if they thought the international community would not respond to what he alleged was their military nuclear programme
UN Secretary General Ban Ki-moon opened Wednesday's proceedings by telling the assembled leaders: "Now is the time to put the 'united' back into the United Nations".
Following Mr Obama, Libya's President Gaddafi fiercely criticised the current power structure of the United Nations, which he said was outdated and unfair, concentrating power unevenly.
Clutching a copy of the preamble to the UN Charter, he said: "It says nations are equal whether they are small or big - are we equal in the permanent seats? No, we are not equal. Do we have the rights of the veto?"
Later, Mr Gaddafi said democracy should not be a luxury for the rich or more powerful.
"All nations should have an equal footing. For those who have a permanent seat, this is political feudalism. It shouldn't be called the Security Council, it should be called the Terror Council."
By tradition dating back to the UN's infancy in the late 1940s, Brazil speaks first after the secretary general opens proceedings
The US, as host country, speaks second
Subsequent speakers are chosen on a first-come, first-served basis
Protocol order is followed: heads of state; heads of government; crown princes; deputy prime ministers; ministers; permanent representatives
However, the order can change up till the last moment
Mr Gaddafi's speech, which continued for more than an hour, was his first address to the UN General Assembly during his 40 years in power.
Relatives of victims of the 1988 Lockerbie bombing protested outside the UN headquarters as Col Gaddafi was due to arrive. The Libyan convicted of the bombing was released from a Scottish prison last month.
The order of the speeches is based on protocol, with some flexibility.
A UN spokeswoman described it as a "challenging and meticulous" task to decide the order.
There is an agreed hierarchy - with heads of state coming before heads of government and crown princes.
But exceptions are made - this time UK Prime Minister Gordon Brown will speak before China's head of state, President Hu Jintao.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.