NEW YORK, N.Y.—The newly-elected Tunisian president vowed Thursday to crack down on Islamist extremists after they encouraged crowds to attack the U.S. embassy in the capital Tunis.

President Moncef Marzouki, in an interview during the annual United Nations General Assembly gathering of world leaders, also called for the Arab League to send a force to Syria.

Marzouki’s promised crackdown on hardline Muslims in Tunisia follows months of struggles by his Islamist-dominated governing coalition to stem a small but aggressive minority of extremists emboldened since the fall of the North African nation’s secular dictator in last year’s revolution, which kicked off the Arab Spring. Salafi extremists have pressured bars to shutter and bullied university campuses to become more conservative, threatening Tunisia’s secular traditions.

“The more we wait, the worse it will become,” Marzouki said. “We have no choice, a crackdown will happen.”

“The Salafis are not just a danger to our democracy, and . . . our image abroad,” Marzouki added, but also to “relations with our friends, the Americans.”

Marzouki has promised that his government will protect the rights of women and religious freedom, while building a robust democracy. But the party also relies on conservative Muslims for votes, and has been reluctant to be associated with a crackdown on the Salafis before elections, expected next year. It is concerned security forces would commit the kind of human rights abuses that were common under the former regime of Zine El Abidine Ben Ali.

Last week, several thousand demonstrators attacked the U.S. embassy, tearing down the American flag and raising one associated with hardline Muslims, while looting and burning buildings. Four demonstrators were killed and dozens injured.

The protest was part of a wave of violent demonstrations around the Muslim world after excerpts of a crude anti-Islam film was dubbed into Arabic and uploaded to YouTube. The protests have led to the deaths of dozens of demonstrators and the U.S. ambassador to Libya, Chris Stevens.

Marzouki said the crackdown would involve arrests of those planning or involved in violent riots.

The president said he cautioned security forces not to engage in torture or other abuses, but conceded that would be difficult to avoid. The former exile said he and many other members of his government were once thrown in jail for their beliefs, and many were harshly interrogated and abused.

“We don’t want to behave like the dictator,” Marzouki said.

Tunisia is rewriting its constitution, which is seen as a test of Islamist influence in newly-democratic Arab nations. Marzouki said the charter would be ready by January, around the second anniversary of the revolution. Marzouki said he would not allow the word “sharia,” or “Islamic law,” to be part of it.

Marzouki is expected to face sharp resistance on blasphemy laws, which he does not want to be part of the constitution, though they enjoy broad political support.

Relations between men and women would be defined by the word “equality,” Marzouki said — and not the term suggested by Islamists, “complimentary.”

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In his speech to the General Assembly on Thursday, Marzouki called for the creation of an international constitutional court to rule on the legality of elections and deter tyrannical regimes.

Marzouki asked the UN to declare dictatorship a “scourge” to be eliminated by a bold program similar to those dedicated to eradicating polio and small pox.