Harper will instead take part in a side event on maternal and child health and attend a talk on the economy hosted by the Canadian American Business Council.
Foreign Affairs Minister John Baird will fill in next week as Canada's voice in the assembly.
"At a time of economic uncertainty, rapid social change and a volatile global environment in which certain regimes are threatening international peace and security and violating the rights of their own citizens, Canada has a vital global role to play in the defence of freedom, dignity and opportunity," Baird said in a statement.
"At this year's General Assembly, Canada will work with its partners to encourage the United Nations to be more accountable, transparent and responsive to the challenges of a changing world."
The delegation to New York also includes International Co-operation Minister Christian Paradis; minister of state for foreign affairs Lynne Yelich; and Deepak Obhrai, Baird's parliamentary secretary.
Meanwhile, a group of former cabinet ministers, senior diplomats, academics and foreign-policy experts is urging the Harper government to re-think how it engages with the UN.
The group held a news conference Monday in Ottawa to outline steps the Conservative government could take to mend what they say is a strained relationship with the world body.
"We're increasingly denying ourselves a place at the table," said Carolyn McAskie, a former assistant secretary general for peacebuilding at the UN.
"We walk out of meetings because North Korea is in the chair. The reason you go to these meetings is so that you can engage all 193 (countries). You don't pick your friends and your enemies. They're all there. You go you play the game. ...
"If you're not at the table, you don't have a voice."
The Canadian delegation has in the past left the room when countries such as Iran are at the podium.
But the foreign-policy experts say Canada's actions at the UN have done its reputation more harm than good.
"Canada couldn't get elected dogcatcher at the United Nations today," said Ian Smilie, who chairs the Diamond Development Initiative.
Canada's relationship with the world body has deteriorated sharply in recent years, he added.
"I don't think any of us could have imagined even three or four years ago that Canada would be in the doghouse as much as it is in relation to the United Nations," Smilie said.
Canada has been critical of the UN since losing a bid for a seat on the Security Council, Smilie said, and the prime minister routinely passes up opportunities to speak to the General Assembly.
"Since we lost our bid to become one of the elected members of the Security Council, we've gone out of our way to be insulting towards the United Nations."
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