The majority of those killed when a gunman opened fire on holidaymakers were British, Tunisia's prime minister has reportedly said.
Five of the 38 dead have so far been confirmed as Britons by Foreign Secretary Philip Hammond, as he warned that number could rise due to the popularity of the area with tourists from the UK.
Tunisian PM Habib Essid has since reportedly told a news conference that the majority of victims were British, followed by Germans, Belgians and other nationalities.
Terror group Islamic State claimed responsibility for the attack in which a young man pulled out a Kalashnikov hidden in a beach parasol and shot at sunbathers in Sousse.
Mr Hammond said yesterday: "We have to assume that a high proportion of those killed and injured will have been British".
SITE Intel Group, which monitors the jihadist threat, tweeted: "#ISIS claimed credit for the Tunisia hotel attack in Sousse and identified the attacker as Abu Yahya al-Qayrawani."
An Irish mother-of-two who was shot dead was named locally as Lorna Carty, from Robinstown, Co Meath.
Family friends said she had taken her husband on holiday to help him recover from heart surgery, and she was believed to have gone to the beach by herself when the gunman went on the rampage.
She was a nurse in a GP surgery in Navan, aged in her 50s, and had a son and daughter. Her husband Declan, a dairy farmer, was said to be uninjured but "absolutely distraught".
David Cameron said the UK stands "shoulder to shoulder" with Tunisia in the battle against terrorism.
The worst such attack in Tunisia's history came on the same day a man was found decapitated after an attack by suspected Islamic extremists on a French factory and a Shiite mosque in Kuwait was bombed killing at least 25 people.
Although the attacks do not appear to be directly linked they come after the so-called Islamic State called for their followers "to make Ramadan a month of calamities for the nonbelievers".
Afzal Ashraf, a consultant fellow at defence and security think tank the Royal United Services Institute, said the attacks may be linked to the anniversary of the declaration of an IS caliphate in Iraq and Syria, which is on Monday.
"If you look at these attacks, and what has been happening over the last 48 hours, attacks by IS in various parts of Syria and Iraq, they want to make a bit of a splash, to get the message out, 'we're still here - it's a year since we declared this thing, and you haven't got rid of us'. They see it as a great victory, because the world has combined against them."
Mr Hammond chaired an emergency Cobra meeting yesterday, and another one will be held this morning to look at the UK's response to the three attacks.
A consular team is in Sousse, and two rapid response teams were travelling to the region overnight, he said.
Bodies covered in blankets were strewn across the beach and medical staff used sun loungers as stretchers to carry away the dead and injured.
At least 36 people were wounded in the attack.
Despite initially believing there was more than one gunman, the Tunisian authorities later said the killer was thought to be a young student who had not previously been known to their security services.
His killing spree on the beach at the Riu Bellevue Park ended when he was shot dead by police. A bomb was found on his body.
British tourist Ellie Makin, from Ripon, North Yorkshire, who was on holiday with her friend Debbie Horsfall from Huddersfield, said the gunman was next to them on a sunbed.
She told ITV News: "He was to the right of me because we were on the last sunbed on the beach. All of a sudden I got up anyway and just happened to look right and all I saw was a gun and an umbrella being dropped.
"Then he started firing to the right hand side of us. If he had fired to the left I don't know what would have happened, but we were very lucky."
Olivia Leathley, 24, was with her boyfriend Mike Jones in her room at the hotel when she heard "loud bangs" from the beach.
They ran to the lobby where they found a woman whose husband had been shot in the stomach in front of her.
Miss Leathley said: "All she said was that he'd been shot and that he was there bleeding on the beach and he was just saying, 'I love you I love you', and then his eyes rolled back into his head. But at that point she was dragged away by people who were trying to keep her safe."
She was thought to be referring to Saera Wilson, who later told the BBC that her fiance Matthew James used his body as a human shield.
She said gas engineer Mr James, 30, from Trehafod, near Pontypridd, was hit in the shoulder, chest and hip.
Speaking from the hospital where Mr James is being treated, Ms Wilson said: "He took a bullet for me. I owe him my life because he threw himself in front of me when the shooting started.
"He was covered in blood from the shots, but he just told me to run away.
"He told me: 'I love you babe. But just go - tell our children that their daddy loves them'.
"It was the bravest thing I've ever known."
Those killed are more likely to be foreign as the local Muslim population is less likely to go to the beach during the holy month of Ramadan.
Tension has been high in Tunisia since an attack on the National Bardo Museum in March which killed 22 people, mostly foreign tourists including a Briton.
A suicide bomber blew himself up in a failed attack on the beach in Sousse in October 2013, while 21 people lost their lives in an attack in the country earlier this year.
Tunisia has undergone unprecedented social and political change since the 2011 uprisings and the Foreign Office says there is a ''high'' threat from terrorism.
Sousse is on the east coast, about 87 miles south of the capital, Tunis. Around 1.2 million tourists visit Sousse every year, drawn by the hotels, sandy beaches and culture.
Downing Street said the Prime Minister will chair a meeting of the Cobra emergency committee this morning and the Government "will do everything we can to help those affected".
It was a bloody day: a wave of attacks across three continents within a matter of hours, leaving more than 60 dead and stoking fresh fears about the threat posed by jihadists claiming affiliation with or inspired by Islamic State, the militant group also known as Isil.
The fact that there are still tourists to attack in Tunisia tells its own story. Ever since it became the birthplace of the Arab Spring in 2011, the tiny north African nation has been the only country in the region to enjoy anything approaching stability after the overthrow of its resident dictator.