UNITED NATIONS — The new presidents of Egypt and Yemen — both of whom were swept to power by uprisings demanding democratic rights — issued clear rebuttals on Wednesday to President Obama’s ardent defense of Western values at the United Nations, arguing that cultural limits on rights like freedom of speech had to be respected.

President Mohamed Morsi of Egypt, who billed his 40-minute speech to world leaders as the first by a democratically elected leader of his country, condemned the violence stemming from a short online video that insulted the Prophet Muhammad and led to numerous deaths, including that of the American ambassador to Libya and three of his staff members.

But Mr. Morsi rejected Mr. Obama’s broad defense of free speech a day earlier at the United Nations, saying “Egypt respects freedom of expression, freedom of expression that is not used to incite hatred against anyone.”

“We expect from others, as they expect from us, that they respect our cultural specifics and religious references, and not seek to impose concepts or cultures that are unacceptable to us,” said Mr. Morsi, a former leader of the Muslim Brotherhood. “Insults against the prophet of Islam, Muhammad, are not acceptable. We will not allow anyone to do this by word or by deed.”