A British woman was among the victims of a deadly shooting at a museum in Tunis, Tunisian health ministry officials said.

The woman has been identified as Sally Jane Adey. The information was confirmed by British Foreign Secretary Philip Hammond, the BBC reported.

"Sadly, I can confirm the death of a British woman in yesterday's terrorist attack in Tunisia. Consular staff are providing assistance to her family. My thoughts are with them at this very difficult time," Hammond said in a statement.

"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.

"I spoke to Prime Minister Habib Essid yesterday to offer my condolences to all those affected by this despicable act and to assure him we stand together against terrorism."

The Foreign & Commonwealth Office (FCO) earlier said two Britons were "caught up" in the attack.Tunisia's health minister also said the death toll of the Bardo Museum shootings has risen to 23 people, including 18 foreign tourists.

Adey was a passenger on a cruise liner that docked in the port city, as part of an off-season Mediterranean cruise the day of the attack.

She was visiting the museum with other tourists on a shore excursion from the MSC Splendida, when the building was stormed.

MSC Cruises initially said that nine passengers were killed and 12 injured in the attack. The company said that, as the ship pulled out to the Mediterranean at sunrise, another six passengers, including a British national, were unaccounted for. It later confirmed the missing Briton was Adey.

"MSC Cruises can confirm that British passenger Sally Adey was tragically killed in yesterday's terrorist atrocities in Tunis. Her husband is receiving support from the MSC Cruises customer care team in Tunis and we will be offering all possible support to him and his family," the cruise line wrote on Facebook.

"At this tragic time, the MSC Cruises family wishes to extend its most sincere and heartfelt condolences to all those who were affected by this tragic event and are suffering as a result, in particular to the families and friends of those who lost their lives as well as the injured ones."

The MSC Splendida had arrived in Tunis on 18 March with 3,714 guests and 1,267 crew aboard.

A number of passengers from another cruise liner, Costa Crociere's Costa Fascinosa, were also among the victims.Costa Crociere said 13 passengers had not returned on board when the ship left Tunis overnight.

Both cruise lines said they have teams in Tunis to coordinate with local authorities and provide assistance to the victims.

Meanwhile, Tunisian Prime Minister Habib Essid has named two suspects in the Tunis Bardo museum massacre that left 19 people dead, most of them foreign tourists, saying one of attackers was known to security services.

Essid said security services flagged up one of the attackers, Yassine Labidi, but not for "anything special". The other gunman was named as Saber Khachnaoui. The prime minister said he was not aware of any links to militant groups such as Islamic State (Isis). Authorities are investigating the backgrounds and motives of the two gunmen in coordination with other governments.

Abidi is a native of Ibn Khaldun, a popular district of Tunis, while the second is from Kasserine, which lies at the foot of Mount Chaambi near the Algerian border. The area is known to be the main hotbed of militant activity in the country.

Both gunmen were killed by security forces in the attack. An interior ministry spokesman told AFP that two or three accomplices are still at large.