In a speech that went well over his allotted five minutes, Sharon urged reconciliation and compromise with Palestinians to end their conflict. But he said that after Israel's withdrawal from the Gaza Strip, it was now up to the Palestinians to "prove their desire for peace."
"The Palestinians will always be our neighbors; we respect them and have no aspiration to rule over them," Sharon said. "They are also entitled to freedom."
The General Assembly hall gave Sharon courteous applause when he finished his speech. Palestinian Foreign Minister Nasser Al-Kidwa sat with his arms folded over his chest.
Meanwhile, Israel and the Palestinian Authority on Thursday said they fear al Qaeda terrorists will infiltrate into Gaza through the open Gaza-Egypt border, where Palestinians and Egyptians have been crossing largely unfettered since Israel withdrew from the area four days ago.
In a deal worked out with Israel, Egypt is supposed to deploy 750 border troops to secure the frontier and prevent weapons smuggling, but neither those troops nor Palestinian policemen have been able to halt the flow of people and arms, including hundreds of assault rifles and pistols.
Israel is worried about mega-terror on its soil and the Palestinian Authority fears that it could be toppled and replaced with an Iranian-style regime, reports CBS News Correspondent Robert Berger.
"We're talking about Iran, we're talking elements in Syria, we're talking about groups like Hezbollah and we're talking also about international terrorist groups like al Qaeda," said Israeli foreign ministry spokesman Mark Regev. Israel has long accused both Iran and Syria of sponsoring militant groups.
Rafiq Husseini, the top aide to Palestinian leader Mahmoud Abbas, said, "we are even more worried than Israel about al Qaeda coming here because al Qaeda will harm us more than Israel." Such a presence, he said, would hurt prospects for peace and renewed negotiations with Israel.
"The Palestinian Authority security apparatus will arrest any suspected al Qaeda members or other terrorist groups if they infiltrate Gaza," he said.