A British tourist was among those killed in the attack on a museum in Tunis, Prime Minister David Cameron said Thursday, vowing to fight against extremists "with everything we have".

"We will not let terrorists undermine democracy," he said in a tweet.

The tourist, named as Sally Adey, was on an excursion to the National Bardo Museum with her husband at the time. He survived the attack, officials said.

"These terrorist attacks yesterday in Tunisia were an appalling and brutal outrage," Cameron said.

"This is the latest example of extremist terror and we have to fight it with everything we have," he said.

"We mustn't let democracy, freedom, the rule of the law, the things we hold dear, and people in Tunisia hold dear, we must not let them be defeated or undermined by these extremists and terrorists."

"That is the battle we are engaged in but I'm confident if we stick to our values we will win through," he added.

At least 20 foreign tourists and two Tunisians died in the attack and 13 passengers from a Costa cruise ship in Tunis on Tuesday are unaccounted for.

In a separate statement, foreign minister Philip Hammond condemned a "despicable act" and said: "The Tunisian people are rightly proud of their democratic transition".

"Cowardly attacks, such as the one we saw yesterday, must not be allowed to undermine what they have achieved," he said. (AFP)