Foreigners have increasingly become targets in Libya's turmoil, where two rival governments are battling for control.
Troops from Niger and Chad recaptured Damasak earlier in March, ending months of control by the Islamist group.
Islamic State militants claimed a suicide bombing that killed seven people at an army checkpoint in the Libyan city of Benghazi on Tuesday and triggered retaliatory air strikes by army forces.
Museum officials said that there have been no threats made against the museum but "we should be vigilant."
Four years after NATO warplanes helped dislodge dictator Muammar Gaddafi, Libya has descended into chaos, with two rival governments fighting for control.
Tunisian security forces have begun a major campaign against extremists after an attack on a Tunis museum left 23 dead.
The U.N. Security Council condemned Houthi rebels for failing to withdraw their forces from the capital.
Those in custody had pledged loyalty to the Islamic State group and were seeking recruits to fight in Iraq and Syria, officials said.
"He won't go very far," President Beji Caid Essebsi says, while acknowledging the country faces a larger jihadist threat.
The attack on the Bardo National Museum that killed 25 was the deadliest terrorist offensive in the country since a 2002 suicide bombing.
Thousands who crossed Egypt's western border to find work have been returning home by land or by flights from Tunisia.
A suicide attack that killed at least 142 pulls Yemen deeper into a region-wide fight, but an ISIS claim is doubtful.
Wednesday's attack in Tunisia heightened the European country's concern that it could be next.
ISIS recently seized control of at least two cities along Libya's Mediterranean coastline after taking territory in Syria and Iraq last year.
Two of the gunmen were killed by security forces during Wednesday's attack on the Bardo Museum in Tunis.
Tunisia's newly elected government needs assistance to fight terrorists, and will likely get it.
The Islamic State group has claimed responsibility for the terrorist attack at a Tunisia museum Wednesday that killed 21 people and injured dozens more.
Social media accounts affiliated with the Islamic State group shared a message that seemed to foretell the attack that killed 20.
The tourism minister said the country remained safe for travelers and denied reports of growing terrorism-related risks there.
The photos, whose authenticity has yet to be verified, show four black-clad men kneeling in an empty street somewhere in Salaheddin province.
Abu Zakariya al-Tunisi was wanted in Tunisia, his homeland, for assassinating two politicians in 2013.
Earlier this month, ISIS fighters reportedly demolished the site of Nimrud, the ancient Assyrian capital located 18 miles south of Mosul.