Speaking to TV news channels, Mrs May said: “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.
“We must work with France and our partners around the world to stand up for our values and for our freedom.”
She added senior officials would be “reviewing what more we can do to ascertain whether there is any further action we need to take” in the wake of the attack.
But she highlighted how the Government has already put extra funding into Britain’s security services and made more cash available to police for counter-terror efforts.
The Prime Minister’s official spokeswoman said security measures were being reviewed at large public events over the next seven days as a “prudent” action.
British consular staff have been sent to Nice to assist any Britons affected by in the attack.
The meeting of the COBRA committee heard that a “small number” of UK nationals had so far been identified as injured in the attack.
The UK’s terror threat level is currently at severe, which means an attack is ‘highly likely’.