It comes after a knifeman reportedly attempted to storm the Houses of Parliament and members of the public were mowed down on the street outside.
Police have since confirmed four people died including a police officer and 20 people were left injured.
Mr Spicer said: “The President has been briefed on the situation in London, he just spoke to Prime Minister May and we’ll have a read-out on the situation.
White House Press Secretary Sean Spicer condemned the attacks and vowed to support the UK
The City of London and her majesty’s Government have the full support of the US Government in responding to the attack and bringing those to justice who are responsible
“We obviously condemn today’s attack in Westminster, which the United Kingdom is treating as an act of terrorism and we applaud the quick response that the British police and their first responders made to the situation.
“The victims are in our thoughts and in our prayers, the City of London and her majesty’s Government have the full support of the US Government in responding to the attack and bringing those to justice who are responsible.”
The statement comes as a car is also believed to have ploughed through a crowd of people on Westminster Bridge shortly after 2.30pm.
Twelve people were reportedly injured before the car continued down towards Parliament, which is believed to have caused people to flee and jump into the Thames to avoid being struck.
London Terror Attack: LIVE PICTURES Wed, March 22, 2017
Two dead, 12 injured as knifeman mows into crowd in Westminster
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Conservative MP Tobias Ellwood (centre) helps emergency services attend to a police officer outside the Palace of Westminster, London
Four people have been confirmed dead following the incident
Reports state the car then reached Parliament where a knifeman got out of the car and attacked a policeman before being shot dead.
The London Ambulance Service confirmed it treated at least 10 people following the incident.
Metropolitan Police Asst Commissioner Mark Rowley said officers believed there to be one suspect but said they were continuing to carry out checks.
Mr Rowley told reporters outside New Scotland Yard: "This was a day we've planned for but hoped would never happen. Sadly it is now a reality."