BEIRUT — Sheikh Hassan Nasrallah, the leader of the militant Hezbollah group, exhorted hundreds of thousands of supporters Monday to keep up the campaign against an anti-Islam video that has unleashed deadly violence and anger at the United States across the Muslim world.

Although the massive, well-organized rally in Beirut was peaceful, protesters set fires near a US military base in Afghanistan, clashed with police in Pakistan, where one demonstrator was killed, and battled with officers outside the US Embassy in Jakarta, Indonesia, the world’s most populous Muslim country.

The turmoil surrounding the low-budget video that mocks the prophet Mohammed showed no sign of ebbing in the week after protesters first swarmed the walls of the US Embassy in Cairo. Four Americans, including the US ambassador to Libya, died amid a demonstration in the eastern Libyan city of Benghazi.

At least 10 protesters have died in the riots, and the targeting of Western diplomatic sites has forced Washington to increase security in several countries. Diplomats at the US Embassy in Beirut destroyed classified material as a security precaution, according to a State Department status report.

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Nasrallah’s appeal for sustained protests could stoke more fury over the video, ‘‘Innocence of Muslims.’’ It was a rare public appearance for Nasrallah, who has been largely out of view since his group battled Israel in a monthlong war in 2006. Fearing Israeli assassination, he has communicated with his followers and gives news conference mostly via satellite link.

He spoke for about 15 minutes before a rapturous crowd estimated by police at 500,000, many with headbands of green and yellow, the colors of Hezbollah.

Nasrallah, who last appeared in public in December 2011 to mark the Shi’ite holy day of Ashoura, warned of repercussions if the United States does not ban the film and have it removed from the Internet.

‘‘The world should know that our anger is not a passing thing. . . . This is the start of a serious campaign that must continue all over the Muslim world in defense of the prophet of God,’’ he said to roars of support. He has called for a series of demonstrations this week to denounce the video.

Hezbollah’s rallies seem aimed at keeping the issue alive by bringing out large crowds. But the group, whose reputation across the Arab world has suffered over its support of the Syrian regime, also appeared to be trying to ensure it did not spiral into violence.

Notably, Hezbollah held Monday’s protest in its own mainly Shi’ite stronghold of Dahieh in south Beirut, far from the US Embassy.

One politician, former President Amin Gemayel of Lebanon, sharply criticized Hezbollah’s call for protests, saying there were no guarantees they would remain peaceful.

Protesters have directed their anger over the film at the US government, insisting it should do something to stop it, although the film was privately produced. American officials have denounced the film for intentionally offending Muslims.

Protests turned violent for the first time in Afghanistan as hundreds of people burned cars and threw rocks at a US military base in the capital, Kabul. Many in the crowd shouted ‘‘Death to America!’’

Afghan religious leaders urged calm after protests broke out in Kabul. ‘‘Our responsibility is to show a peaceful reaction, to hold peaceful protests. Do not harm people, their property or public property,’’ said cleric Karimullah Saqib.

On the main thoroughfare through the city, demonstrators burned tires, shipping containers and at least one police vehicle before they were dispersed. Police shot in the air to prevent about 800 protesters from pushing toward government buildings downtown.

More than 20 police officers were slightly injured, most by rocks.

Several hundred demonstrators in northwestern Pakistan clashed with police after setting fire to a press club and a government building, said police official Mukhtar Ahmed. The protesters apparently attacked the press club in Khyber Pakhtunkhwa province’s Upper Dir district because they were angry their rally wasn’t getting more coverage, he said.