Britain will stand "shoulder to shoulder" with France and redouble its own efforts against terrorism, Prime Minister Theresa May said today.

May warned that a terrorist attack is highly likely in the UK following Thursday's attack in Nice, during which 84 people were killed when a gunman drove a heavy lorry into crowds celebrating Bastille Day in the French Riviera city.

May condemned the "horrifying" attack and said: "The threat level here in the United Kingdom is already at severe – that means that a terrorist attack is highly likely.

"Senior officials today will be reviewing what more we can do to ascertain whether there is any further action we need to take."

"If as we fear, this was a terrorist attack then we must redouble our efforts to defeat these brutal murderers who want to destroy our way of life," the PM added, noting that more funding was already being made available for security services in the UK.

"Of course we always look at these issues – we have been living with a severe threat level for some time now – but today our thoughts must be with those people in France, with the people of France, and all those who have lost their loved ones or have been injured in this attack," she said.

French newspaper Nice-Matin said local sources had identified the truck driver as 31-year-old Mohamed Lahouaiej Bouhlel.

He was killed after engaging in gunfire with police at the scene.

Bouhlel was married with three children, and came from the Tunisian town of Msaken. Tunisian security sources said he was not known by authorities there to hold radical or Islamist views, though he was known to French police in connection with common crimes including theft and violence.

Sources said the attack appears to have been premeditated.

Interior Minister Bernard Cazeneuve said 18 people were in a critical condition after the attack, and the dead included several children. The US State Department said two American citizens had been killed, while Russian student Viktoria Savchenko was also among the dead.

French President Francois Hollande said in a pre-dawn address that he was calling up military and police reservists to relieve forces worn out by enforcing a state of emergency begun in November after Islamic State gunmen and suicide bombers struck Paris entertainment spots on a Friday evening, killing 130 people.

Only hours earlier he had announced the emergency would be lifted by the end of July. Following the attack, he said it would be extended by a further three months.

"France is filled with sadness by this new tragedy," Hollande said. "There's no denying the terrorist nature of this attack."

Major events in France have been guarded by troops and armed police since the November 13 attacks in Paris, but it appeared to have taken many minutes to halt the progress of the truck as it tore along pavements and a pedestrian zone just after 10.30pm last night.

One witness said she thought the attacker was firing a gun as he drove.

"I saw this enormous white truck go past at top speed," said Suzy Wargniez, a local woman aged 65 who was watching from a cafe on the promenade. "It was shooting, shooting."

A local government official said weapons and grenades were later found inside the vehicle.

Nice-Matin said on Twitter that police were searching the attacker's home in the Nice neighbourhood of Abattoirs. It gave no source of the information.

Islamic State targets France

After the Paris attacks, Islamic State said France and all nations following its path would remain at the top of its list of targets as long as they continued "their crusader campaign", referring to action against the group in Iraq and Syria.

France is conducting air strikes and special forces operations against ISIS, as well as training Iraqi government and Kurdish forces.

"We will further strengthen our actions in Syria and Iraq," Hollande said, calling the tragedy – on the day France marks the 1789 revolutionary storming of the Bastille prison in Paris – an attack on liberty by fanatics who despised human rights.

On social media, Islamic State supporters celebrated the high death toll and posted a series of images, one showing a beach purporting to be Nice with white stones arranged to read "IS is here to stay" in Arabic.

Hiding in terror

Nice-Matin journalist Damien Allemand had been watching the firework display when the truck tore by. After taking cover in a cafe, he wrote on his paper's website about what he saw: "Bodies every five metres, limbs ... Blood. Groans."

"The beach attendants were first on the scene. They brought water for the injured and towels, which they placed on those for whom there was no more hope."

Officials have warned of the continuing risk of Islamist attacks in Europe. Reverses for Islamic State in Syria and Iraq have raised fears it might strike again, using alienated young men from the continent's Arab immigrant communities.

Nice, a city of 350,000, has a history as a flamboyant, aristocratic resort but is also a gritty metropolis. It has seen dozens of its Muslim residents travel to Syria to fight.

"Neither the place nor the date are coincidental," a former French intelligence agent and security consultant, Claude Moniquet, told France-Info, noting the jihadist presence in Nice and the fact that July 14 marks France's revolution.

"Tragic paradox that the subject of Nice attack was the people celebrating liberty, equality and fraternity," European Council President Donald Tusk said on Twitter.

At Nice's Pasteur hospital, medical staff were treating large numbers of injuries. Waiting for friends who were being operated on, 20-year-old Fanny told Reuters she had been lucky.

"We were all very happy, ready to celebrate all night long," she said. "I saw a truck driving into the pedestrian area, going very fast and zig-zagging.

"The truck pushed me to the side. When I opened my eyes I saw faces I didn't know and started asking for help ... Some of my friends were not so lucky. They are having operations as we speak. It's very hard, it's all very traumatic."

British Foreign Secretary Boris Johnson said on Friday he was shocked and saddened by the attack. 

"Shocked and saddened by the appalling events in Nice, and the terrible loss of life," Johnson, the former London mayor, said on Twitter.