The United States has ordered non-essential diplomatic staff and their families to leave Sudan and Tunisia.
In a statement, the state department also urged US citizens in Tunisia to make their way out of the country.
The US embassies in the Tunisian and Sudanese capitals have both been attacked in the wave of anti-US protests in the Muslim world over an anti-Islam film made in the US.
Earlier, Sudan refused to allow the US to send Marines to protect its embassy.
Sudanese officials said the country's security forces were capable of providing protection to the embassy.
Three people were killed when the US embassy was attacked in Khartoum on Friday. The German and UK missions were also singled out by protesters.
The state department said the Sudanese government had "taken some steps to limit the activities of terrorist groups", but that elements remained and had threatened to attack Western interests, the BBC's Paul Adams in Washington reports.
Americans were also warned against all travel to Tunisia, after two people lost their lives during attacks on the embassy in Tunis and a neighbouring American school.
"US citizens remaining in Tunisia should use extreme caution and avoid demonstrations," it said.
The Canadian government announced on Sunday it was closing its embassies in Sudan, Libya and Egypt for the day as a precautionary measure.
Several other people have been killed across the Middle East and north Africa since the protests over the film erupted on Tuesday. The US ambassador to Libya, Chris Stevens, and three other US officials died when the consulate building in Benghazi was attacked and set on fire.
The US and Canadian announcements came as Al-Qaeda in the Arabian Peninsula called for fresh attacks against Western embassies.
"What has happened is a great event, and these efforts should come together in one goal, which is to expel the embassies of America from the lands of the Muslims," the group said in a statement, according to the Associated Press.
Earlier on Saturday, Egyptian Prime Minister Hisham Qandil said in an interview with BBC Arabic that the US must do all it can to stop people insulting Islam.
Mr Qandil said it was "unacceptable to insult our Prophet" but also not right for peaceful protests to turn violent.
"Egyptians, Arabs, Muslims - we need to reflect the true identity of Muslims, how peaceful they are, and talk to the Western media about the true heart of the Muslims, that they condemn violence," said Mr Qandil.
He also called on the US, and other governments, to "take the necessary measures to ensure insulting billions of people, one-and-a-half billion people and their beliefs, does not happen and people pay for what they do."
The exact origin of the film and motivation behind it are still unclear and much misleading information has been circulated about its production.
The original posting of a 14-minute trailer for the film on YouTube came from an account linked to the name 'sambacile'.
No film-maker by the name of Sam Bacile has been traced, and the US authorities are now trying to establish whether Nakoula Basseley Nakoula, who has admitted involvement in the film, posted it under pseudonym.
On Saturday, he was taken from his home in California and questioned by US investigators over whether he had broken the terms of his probation for a previous fraud conviction.
Nakoula was freed on probation in June 2011 on condition that he did not use the internet without authorisation or assume aliases.
He was released by police after questioning and may have gone into hiding, the Associated Press reports.
The right to freedom of speech is enshrined in the first amendment of the American constitution and while the video has been widely condemned in the US, the filmmakers are not believed to have committed any punishable crime, the BBC's Alistair Leithead in Los Angeles reports.
Any portrayal of the Prophet is considered blasphemous to Muslims, and the film, a low-budget, amateurish production called Innocence of Muslims, depicts him as a womaniser and leader of a group of bloodthirsty men.
It also touched on themes of paedophilia and homosexuality.
Calls for calm
Angry protests have also erupted in several other countries including Yemen, Lebanon, Somalia, Iraq, Pakistan and Turkey.
There were clashes between Muslim protesters and police in Sydney, Australia on Saturday over a wide area of the city centre.
Police used pepper spray to disperse the crowds as they tried to enter the US consulate building. A number of arrests were made during the clashes.
On Saturday, insurgents attacked Nato's heavily fortified Camp Bastion base in southern Afghanistan, killing at least two US Marines. The Taliban told the BBC it had carried out the attack in revenge for the film.
In Belgium, police in Antwerp said around 120 people were detained after clashes, blamed on a group called Sharia4Belgium.
The mostly young protesters chanted slogans such as "Obama go to hell" and "Hollywood go to hell", Reuters news agency reports. Those held were expected to be released after identity checks, a spokesman said.
Western and Middle Eastern leaders have called for calm.
Grand Mufti Sheik Abdel-Aziz al-Sheik, the highest religious authority in Saudi Arabia, said Muslims should "denounce it without anger".
"Muslims should not be dragged by wrath and anger to shift from legitimate to forbidden action and by this, they will, unknowingly, fulfil some aims of the film," the Associated Press news agency quoted him as saying.
The European Union has urged leaders in Arab and Muslim countries to "call immediately for peace and restraint".