By Edith Honan

NEW YORK (Reuters) - Egypt's new Islamist president Mohamed Mursi delivered a call on Tuesday for "genuine cooperation" between cultures, but in the wake of violent assaults on U.S. diplomatic missions in the Muslim world he also cautioned that a joke in one culture may not be funny in another.

Speaking at a philanthropic meeting convened in New York by former U.S. President Bill Clinton, Mursi signaled an embrace of multiculturalism as an alternative to a single culture seeking dominance.

"The world cannot become one culture or one civilization. However, can we have civilizations that live side by side, not against one another? It is possible," said Mursi. "Maybe a joke in one country is not funny in another country. That's the nature of culture."

Mursi's speech, one day before he is to address the United Nations General Assembly, came at a delicate time for relations between the United States and Egypt.

Once strong allies, the relationship has been strained in the aftermath of Egypt's pro-democracy uprising, which ousted autocratic President Hosni Mubarak.

An anti-Islam film posted on YouTube provoked protests across the Muslim world this month. Related violence included the storming of U.S. and other Western embassies, the killing of the U.S. ambassador to Libya and a suicide bombing in Afghanistan.

The anti-American protests have cast new shadows over U.S. engagement with the region, and President Barack Obama said in a recent interview that the United States considered Egypt's Islamist government neither an ally nor an enemy.

Mursi, who was elected in June, recently told The New York Times that Washington must change its approach to the Arab world and help build a Palestinian state to reduce pent-up anger in the region.

Mursi addressed the controversy over the YouTube film directly, calling it a work of "religious defamation." He said that while as a Muslim he viewed human life as sacred, he added that "physical violence is not the only form of violence."

"While we must acknowledge the importance of freedom of expression, we must also recognize that such a freedom comes with responsibilities especially when it has serious implications for international peace and security," he said.

He also challenged the international community to develop a new model of global governance that would aid the world's needy and promote dignity.

"I simply cannot watch the blood that's shed in Syria or the children that are starving in Gaza and claim that our model of global governance works," Mursi said.

(Additional reporting by Leah Schnurr; Editing by Christopher Wilson)