Unrest across the Middle East is set to dominate discussion at the summit.
Mr Obama also again stressed the US would not allow Iran nuclear weapons.
He said the US would "do what we must" to stop Tehran acquiring nuclear arms. Six weeks before the US election, the president said a nuclear-armed Iran was "not a challenge that can be contained".
Iran's nuclear programme and the 18-month conflict in Syria have featured strongly in Tuesday's speeches at the Assembly, as have the recent protests across the Muslim world in response to a US-made video mocking the Prophet Muhammad.
"It is time to marginalise those who - even when not resorting to violence - use hatred of America, or the West, or Israel as a central principle of politics," said Mr Obama.
The brand of politics that pits East against West, South against North, Muslim against Christian, Hindu and Jew, could not deliver the promise of freedom, he added.
"That brand of politics only makes it harder to achieve what we must do together: educating our children and creating the opportunities they deserve; protecting human rights and extending democracy's promise.
"Today, we must declare that this violence and intolerance has no place among our United Nations."
Syria's conflict is not formally on the General Assembly's agenda but was a focal point of discussion on the opening day.
He called for action from the divided UN Security Council and said "the international community should not look the other way as violence spirals out of control".
"Brutal human rights abuses continue to be committed, mainly by the government but also by opposition forces," he added.
People did not look to the UN to be simply a mirror reflecting back a divided world, said Mr Ban. Rather, they wanted to see it come up with solutions to problems.
The US president was blunter in his assessment of Syria, saying Bashar Assad's regime must end.
The UN Security Council has been unable to reach agreement on the Syria crisis and on Monday UN envoy Lakhdar Brahimi warned that the situation was "extremely bad and getting worse".
While he did not have a full plan, he said he had "a few ideas". Mr Brahimi has just visited Damascus as well as refugee camps in neighbouring Jordan and Turkey.
The BBC's Barbara Plett says that diplomats have played down expectations for Mr Brahimi's mission, with no sign of fundamental divisions on the council being bridged.
Mr Hollande, in his first appearance at the assembly, is also expected to call for backing for an international force to be sent to the West African state of Mali to help dislodge Islamist militants who have taken over the north of the country.
Although the White House said Mr Obama's address was not a campaign speech, it follows critical remarks about his foreign policy from Republican presidential candidate Mitt Romney.
His presidential rival condemned Mr Obama's description of the murder of Mr Stevens and three other Americans as "bumps in the road". He has also castigated him for not taking time out to hold talks on Iran during the summit with Israeli PM Benjamin Netanyahu.
Mr Obama has rejected the Israeli leader's calls for Washington to set Tehran "red lines".
Instead, he said the United States would "do what we must to prevent Iran from obtaining a nuclear weapon" with the backing of "a coalition of countries" holding Tehran accountable.
Mr Netanyahu has recently appeared on US television to press for a tougher line on Iran, and he will take the same message to the General Assembly on Thursday.
Tehran says its nuclear programme is for civilian purposes.
On the eve of the assembly, Iranian President Mahmoud Ahmadinejad told a UN meeting that Israel was a "fake regime", prompting Israel's UN ambassador, Ron Prosor, to walk out.
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