US President Barack Obama has said the world must tackle stark challenges, and the US cannot face them alone. In his first speech to the UN General Assembly, he said global problems included nuclear proliferation, war, climate change and economic crisis.
All nations bore responsibility for addressing these problems, he said.
Later, in a long speech, Libyan leader Muammar Gaddafi berated the UN Security Council, while French President Nicolas Sarkozy issued a stern warning to Iran.
We must build new coalitions that bridge old divides... All nations have rights and responsibilities - that's the bargain that makes this work 
US President Barack Obama
UN General Assembly
Iranian President Mahmoud Ahmadinejad, who has previously said he does not believe the Holocaust happened, was due to speak later on Wednesday.
Israel has called for a boycott of his appearance and the Germans have said they will walk out if he repeats the claim.
'Act together'
In his maiden speech to the forum of leaders from more than 120 nations, Mr Obama acknowledged the expectations that accompanied his presidency - expectations, he said, which were "not about me".
UN SPEECHES ON WEDNESDAY
US President Obama
Libyan Col Gaddafi
UK Prime Minister Brown
Russian President Medvedev
Iranian President Ahmadinejad
UN Assembly: Key Issues Big week for Obama at UN Protests meet Gaddafi
He said that when he took office, "many around the world had come to view America with scepticism and mistrust".
He said some of this was based on "misperceptions" but it was also due to "opposition to specific policies".
But Mr Obama said "no world order which elevates one nation above others" could succeed in tackling the world's problems.
"Those who used to chastise America for acting alone in the world cannot now stand by and wait for America to solve the world's problems alone," he said.
"We must build new coalitions that bridge old divides... All nations have rights and responsibilities - that's the bargain that makes this work."
MARDELL'S AMERICA
Obama's speech to the United Nations was a reminder of the scale of his ambition and the intractability of the problems before him
Mark Mardell
BBC North America editor
Read Mark's thoughts in full
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".
'Terror Council'
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."
SPEAKER PROTOCOL
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.
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