In a wide-ranging address that touched on all major issues confronting the region, Morsi also decried Israeli settlement-building on territory Palestinians claim for a future state and condemned a film produced in the US that denigrates Islam's Prophet Muhammad.
He urged all UN member nations to join in an effort to end what he called "the catastrophe in Syria" that pits the regime of Bashar al-Assad against opposition forces trying to end 40 years of dictatorship. More than 30 000 people have been killed in the 18-month conflict.
Morsi has called for Assad to step down and said on Wednesday that "the bloodshed in Syria and the humanitarian crisis that has unfolded must be stopped".
Morsi, an Islamist and key member of the once-banned Muslim Brotherhood, opened his remarks to the UN general assembly by celebrating himself as Egypt's first democratically elected leader who was swept into office after what he called a "great, peaceful revolution" that overthrew Hosni Mubarak.
He then quickly inserted himself into the thorniest issues in the Middle East, demanding that the United Nations grant membership to the Palestinians, with or without a peace agreement with Israel.
"The fruits of dignity and freedom must not remain far from the Palestinian people," he said, adding that it was "shameful" that UN resolutions are not enforced.
The Palestinians are expected to again ask for UN recognition and formally make application to the world body in November, after the US presidential election.
US President Barack Obama said when the Palestinians sought recognition last year that Washington would block the move until there was a peace deal with Israel. The focus of Israel-Palestine negotiations, which have been on hold for four years, is a two-state solution that would formally grant the Palestinians the rights of an independent country.
In his bid to end the violence in Syria, Morsi has invited Turkey, Iran and Saudi Arabia to join a contact group, though the Saudis have not yet participated and the fighting in Syria continues unabated. While Morsi wants Assad to step aside, he said Wednesday that he opposes any foreign military intervention.
The UN Security Council, which could call for intervention or global sanctions against Syria, is deadlocked because Russia, Assad's main protector, and China have blocked a series of resolutions brought by Western governments.
Morsi also denounced as an obscenity the anti-Islam video that portrays the Prophet Muhammad as a womaniser, a child molester and a fraud, insisting that freedom of expression does not allow for attacks on any religion.
He also condemned the violence that swept Muslim countries last week in reaction to the video. At least 51 people were killed, including the US ambassador to Libya and three other Americans targeted in an attack on the US Consulate in Benghazi.
"Egypt respects freedom of expression. One that is not used to incite hatred against anyone. One that is not directed toward one specific religion or culture. A freedom of expression that tackles extremism and violence. Not the freedom of expression that deepens ignorance and disregards others," Morsi said.
He appeared to have been responding to Obama's general assembly speech on Tuesday in which the US leader again condemned the video but sternly defended the US Constitution's free speech guarantees.
In Cairo, Egyptians watched Morsi's speech closely for signs of how he would conduct his presidency. Sahar Abdel-Mohsen, a 31-year architect, praised Morsi's condemnation of the Assad regime, but questioned his assertions about free speech.
"How can he talk about freedom of expression when there are many protesters in detention in Egypt, including minors, and when people are locked up for the so-called contempt of religion?" she said.
The head of the Arab League, meanwhile, called for the international community to criminalise blasphemy, warning that insults to religion pose a serious threat to global peace and security.
Nabil Elaraby's comments to a special session of the UN Security Council put him at direct odds with the US and its Western allies, which are resolutely opposed to restrictions on freedom of expression. Elaraby said that if the West has criminalised acts that result in bodily harm, it must also criminalise acts that cause "psychological and spiritual harm".
Earlier on Wednesday, Iranian leader Mahmoud Ahmadinejad, known for past fiery denunciations of the US and Israel, spoke at length about his vision for a new world order without the "hegemony of arrogance".
Of Israel, he cited what he termed the "continued threat by the uncivilised Zionists to resort to military action against our great nation".
The US delegation boycotted Ahmadinejad's speech in response to the "paranoid theories and repulsive slurs against Israel" included in a separate address delivered by the Iranian president on Monday.
"It's particularly unfortunate that Mr Ahmadinejad will have the platform of the UN General Assembly on Yom Kippur, which is why the US has decided not to attend," Erin Pelton, spokesperson for the US Mission to the UN, said in a statement.
Thousands of protesters in yellow vests emblazoned with photos of Iranian dissidents they said were killed by the Iranian regime gathered outside UN headquarters during the Iranian leader's speech. Speakers included former House Speaker Newt Gingrich, Representative Carolyn Maloney, D-NY, and former Representative Patrick Kennedy, D-R.I.
In his speech on Wednesday, Ahmadinejad did not refer to Iran's nuclear programme. Israel and Western nations contend that Tehran is using what it insists is a peaceful nuclear programme as a cover for developing the ability to build atomic weapons.
Tough sanctions have been imposed on Iran as punishment for its failure to cooperate with the UN nuclear watchdog agency to prove the peaceful nature of its drive to enrich uranium to levels that could be used to build a nuclear weapon.
Israel has threatened a military strike against Iranian nuclear installations but Obama insists there is still time to solve the dispute through diplomacy. He has vowed to stop Tehran from obtaining a nuclear arsenal.
Outside the UN, Alex Mohammed (40) a restaurant manager from Chicago, stood next to a mock jail cell with a noose next to it, and a cartoon of Ahmadinejad standing under a series of hanged Iranians' legs and the inscription: "We don't have political prisoners in Iran – anymore."
"It's getting worse in Iran, because the dictator is taking away more freedoms, including freedom of speech, and jailing journalists," said Mohammed, who has family in Tehran. – Sapa-AP