"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," Obama said.
"Now is the time for all of us to take our share of responsibility for a global response to global challenges."
Obama said past policies and a perception of unilateralism by the United States had fed "an almost reflexive anti-Americanism" that too often was used as an excuse for inaction.
"The time has come for the world to move in a new direction," Obama said before a U.N. chamber packed with more than 100 of his global counterparts.
The president offered a litany of policy changes and actions his administration had undertaken during his first nine months in office, with the overarching message that the United States has no interest in a go-it-alone stance and instead wants to act as an equal partner with others on the world stage.
"In an era where our destiny is shared, power is no longer a zero-sum game," Obama said. "No world order that elevates one nation or group of people over another will succeed."
Obama received hearty applause when he entered the room, from even the likes of Libyan leader Moammar Gadhafi, and his address was interrupted several times by polite applause. Iranian President Mahmoud Ahmadinejad did not join in the applause.
Gadhafi addressed the General Assembly immediately after Obama, but White House aides made sure the two leaders would not cross paths. Tensions with the Libyan leader are high in the wake of Scotland's recent release of Libyan Abdel Baset al-Megrahi, who was convicted of the 1988 bombing of Pan Am Flight 103, in which 270 people died.
In his speech, Obama summoned fellow leaders to do their part to address a long list of global challenges: to help bring about a nuclear weapons-free world, to increase security from terrorists and promote peace between Israelis and Palestinians, to tackle climate change and to create more economic opportunity. In essence, Obama's message was that he expects plenty in return for reaching out.
"If we are honest with ourselves," he told world leaders, "we need to admit that we are not living up" to the shared responsibility to meet such challenges.
"Extremists sowing terror in pockets of the world," Obama said. "Protracted conflicts that grind on and on; genocide; mass atrocities; more nations with nuclear weapons; melting ice caps and ravaged populations; persistent poverty and pandemic disease."
"I say this not to sow fear, but to state a fact: The magnitude of our challenges has yet to be met by the measure of our actions," Obama said.
He said that Iran and North Korea must be held accountable if they continue to put their pursuit of nuclear weapons ahead of international security.
"The world must stand together to demonstrate that international law is not an empty promise and that treaties will be enforced," he said.
Obama has said the door is open to Iran to discuss the issue, but that U.S. patience is not limitless. He has taken the same position with respect to the reclusive communist regime in North Korea.
Seeking to build on his three-way meeting in New York on Tuesday with Israeli and Palestinian leaders, Obama urged nations aligned with either side to join the cause of advancing Mideast peace - by speaking honestly to Israelis about Palestinian's legitimate claims and to Palestinians and Arab nations about Israel's right to exist.
"All of us must decide whether we are serious about peace, or whether we only lend it lip-service," Obama said. "To break the old patterns, to break the cycle of insecurity and despair all of us must say publicly what we would acknowledge in private."
On the warming planet, Obama said "the danger posed by climate change cannot be denied - and our responsibility to meet it must not be deferred."
The president said he understood the temptation of nations to put economic recovery ahead of efforts to address climate change, but said that must not be allowed to happen.
Ahead of the G-20 meetings of industrial and developing nations that Obama is hosting later this week in Pittsburgh, he lobbied for stronger financial regulations - "new rules of the road" - to prevent future economic calamities. Momentum for such changes has fallen off as the economy appears to be limping back to health.
While Obama's summons for world leaders to work together is hardly new, it is sharper because of the political context. Obama follows Bush, who at times questioned the U.N.'s toughness and credibility, particularly in containing Iraq's Saddam Hussein.
Obama's team is intent on drawing the contrast.
"The United States has dramatically changed the tone, the substance and the practice of our diplomacy at the United Nations," said Susan Rice, Obama's ambassador to the U.N.
Obama started his day with his first meeting with the new Japanese prime minister, Yukio Hatoyama, who has said he wants to shift Japan's diplomatic stance from one that is less centered on Washington's lead.
Obama and Hatoyama said after their talks that the traditional alliance between their nations will continue. Hatoyama's sometimes anti-Washington remarks weren't mentioned directly.
Later, Obama was meeting with Russian President Dmitry Medvedev. That session comes just days following Obama's decision to abruptly scrap a Bush-era missile defense plan that Russia deeply opposed, swapping it for a proposal the U.S. says better targets any launch by Iran.