Two Spanish holidaymakers - including a pregnant woman - have been found hiding in the museum in Tunisia, where 23 people were killed in an attack yesterday.
Tunisia's health minister said the number of people who died in the attack had risen to 23, including the two gunmen.
Terrorist group Islamic State has released an online audio recording in which it claims responsibility for the killings.
A statement released by Tunisia's presidency said nine people suspected of links with the gunmen had been arrested. It said the nine included four people directly linked to the operation and five suspected of having ties to the cell.
Witnesses say the gunmen behind the attack opened fire on tourists arriving at the capital's Bardo Museum, renowned for its collection of Roman mosaics, before chasing them inside.
Many of the victims - including British, Japanese, Italian, Colombian, Spanish, Australian, Polish and French nationals - were passengers on two cruise liners which had recently arrived in Tunis.
The two attackers were among the 23 people left dead.
In an interview with France's RTL radio, Mr Essid said Tunisia was working with other countries to learn more about the attackers, identified as Yassine Laabidi and Hatem Khachnaoui.
The pair were killed by security services in a raid after the attack.
Mr Essid said Laabidi had been flagged to intelligence, although not for "anything special."
British Foreign Secretary Philip Hammond said: "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.
"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," he added.
Spain's foreign minister, Jose Manuel Garcia Margallo, also revealed a Spanish tourist couple were found safe after hiding out in the Tunis museum all night after the attack.
He said the pair - Juan Carlos Sanchez and Cristina Rubio, who is four-months pregnant - were so afraid that they did not want to move.
MSC Cruises said nine people who had been sailing on its vessel, Splendida, were killed in the attack and 12 were injured.
The company said: "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."
Originally posted at 9.13am
