At least one protester was killed in violent protests in Pakistan and thousands attended an angry rally in the Philippines city of Marawi.
Weapons were fired and police cars torched in the Afghan capital, Kabul.
The leader of Lebanon’s Hezbollah has said the US faces “very dangerous” repercussions if it allows the full video to be released.
In a rare public appearance, Sheikh Hassan Nasrallah told a rally in the capital Beirut that the world did not understand the “breadth of the humiliation” caused by the “worst attack ever on Islam”.
Thousands of people were on the streets, waving flags and chanting: “America, hear us – don’t insult our Prophet”.
Sheikh Hassan Nasrallah, the influential leader of the Shia Muslim militant group, earlier called for a week of protests – not only against American embassies, but also to press Muslim governments to express their own anger to the US.
A trailer for the obscure, poorly made film at the centre of the row, entitled Innocence of Muslims, came to light in recent weeks and protests first erupted in the Egyptian capital, Cairo, last Tuesday.
More than a dozen people have died in protests since.
In Pakistan’s Khyber Pakhtunkhwa province, the local press club was burnt down and government offices attacked in the Upper Dir district.
One protester was killed in an exchange of fire with police, following the death of another protester on Sunday.
A protest of thousands of students took place in the nearby city of Peshawar, reported AFP news agency.
In the biggest city, Karachi, police fired in the air to disperse a crowd heading for the US consulate, reported Reuters, and lawyers marched in Lahore.
Former British Prime Minister Tony Blair said the film was “wrong and offensive but also laughable as a piece of film-making – what is dangerous and wrong is the reaction to it”.
Tony Blair, who now serves as a Middle East peace envoy, said the protests were ultimately about the “struggle of modernization” under way in the region and not “some form of oppression by the West”.
The exact origins of the film are shrouded in mystery, although US authorities say they believe the film was made by Nakoula Basseley Nakoula, a convicted fraudster living in California who has since been questioned over his role.
A trailer of the film is available on YouTube and the company said it would not remove it as it was within its guidelines.
But a spokesperson said YouTube had restricted access to the clip in countries where its content is illegal “such as India and Indonesia as well as in Libya and Egypt given the very sensitive situations in these two countries”.
The eruption of anger has seen attacks on US consulates, embassies and business interests across the Middle East and North Africa. British, Swiss, German and Dutch properties have also been targeted.
The US ambassador to Libya was among four Americans killed on the day protests first broke out.
Libyan Interior Minister Fawzi Abdul Al has dismissed a claim on Sunday by the president of the national congress that 50 people have been arrested in connection with the deaths.
He said only four people had been detained so far, although up to 50 could be under investigation.
• About 3,000 protesters burned US and Israeli flags in the southern Philippines city of Marawi
• In Yemen, hundreds of students in the capital, Sanaa, called for the expulsion of the US ambassador, said AFP
• In Indonesia’s capital, Jakarta, hundreds of protesters faced off with police, throwing stones and petrol bombs, while police retaliated with tear gas
• More protests were reported in Srinagar, Indian-administered Kashmir
• Hundreds of Palestinians staged a peaceful sit-in protest in the West Bank city of Ramallah
• Angry demonstrators in the Afghan capital, Kabul, fired guns, torched police cars and shouted anti-US slogans
• A small protest was held outside the US embassy in Azerbaijan’s capital, Baku, AP reported.
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