Two Tunisians, a police officer among them, also died in Wednesday's attack.
Both gunmen were also killed. A search is on for suspects linked to them.
Two or three accomplices are still at large, an interior ministry spokesman told AFP news agency. The spokesman said both attackers were "probably" Tunisian. The second gunman has been named as Hatem Khachnaoui.
The tourists killed in the attack include visitors from Japan, Italy, Colombia, Australia, France, Poland and Spain, officials said.
Tunisia's health minister said a British woman had also been killed, but gave no further details.
On Thursday, three people - two Spanish tourists and one Tunisian museum worker - were found at the museum after having hidden there overnight, police said.
Officials say more than 40 people, including tourists and Tunisians, were injured. The gunman were killed after holding tourists hostage for several hours at the museum.
Speaking after the attack on national TV, Tunisia's President Beji Caid Essebsi said the country would not be cowed by terror attacks.
"These monstrous minorities do not frighten us," he said. "We will resist them until the deepest end without mercy."
At the time of the attack, deputies in the neighbouring parliament building were discussing anti-terrorism legislation.
Sayida Ounissi, an MP, told BBC Radio Four's Today programme that the security services had said the gunmen had originally planned to attack parliament.
A statement released by a jihadist media outlet gave a similar account, saying the gunmen began killing tourists after being repelled by police at the parliament. The statement did not say which group carried out the attack.
Many Tunisians took to the streets of central Tunis to protest against the attack, waving flags and lighting candles outside the museum.
World leaders condemned the attack and expressed their support for Tunisia's counter-terrorism efforts.
The UN Security Council issued a statement saying no terrorist action could reverse Tunisia's path towards democracy. The statement offered condolences to those affected by the attack, and called for the perpetrators to be brought to justice.