Tunisia's interior ministry threatened to punish all those involved in Friday's US embassy attack that left four people dead and 49 injured after extremist protesters angry over the amateur film made in the United States stormed the installation.
Two protesters were killed in Sudan on Friday as around 5,000 furious demonstrators attacked the embassies of Britain, the United States and Germany, setting the latter mission ablaze.
"Given the security situation in Tunis and Khartoum, the State Department has ordered the departure of all family members and non-emergency personnel from both posts, and issued parallel travel warnings to American citizens," State Department spokeswoman Victoria Nuland said in a statement.
In a travel warning, the State Department urged US citizens to "avoid all public demonstrations and political rallies, as even demonstrations that seem peaceful can turn confrontational and become violent with little or no notice."
"You should keep a low profile, vary your times and routes of travel, exercise care while driving and ensure that your passport and Sudanese visa are always valid and up to date," it added.
The warning, which replaced a similar notice issued on September 7, noted that while Sudan has taken "some steps" to limit the activities of extremist groups, "elements of these groups remain in Sudan and have threatened to attack Western interests."
It said the terror threat remains "critical" in Sudan, where enhanced security measures are in place for US government personnel, who are now required to travel in armored government vehicles for official business and to obtain advance permission for travel outside of Khartoum.
Washington also ordered the departure of all non-emergency US personnel from Tunisia following Friday's attack.
"The Department of State warns US citizens against all travel to Tunisia at this time," it added in a travel warning for that country.
"US citizens remaining in Tunisia should use extreme caution and avoid demonstrations, make their own contingency emergency plans" and inform the embassy of their presence and contact information, the notice added.
Protests over a trailer for the anti-Islam film on YouTube first broke out on Tuesday in Egypt and Libya, where an armed mob assaulted the US consulate in Benghazi in an attack that killed the US ambassador and three other Americans.
The demonstrations have since spread across other Muslim-majority nations in North Africa, the Middle East, Africa and Asia. Dozens of men, women and children also protested near the US embassy in Paris on Saturday.
Sudan and Yemen have rejected a US request to send Marine counterterrorism units to those countries to protect the US diplomatic posts.
