Protests over the film have swept the Arab world
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, reports the BBC.
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.
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 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."
Meanwhile, a man suspected of being involved in making in the film has been questioned by US investigators over whether he has broken the terms of his probation for a previous fraud conviction.
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.