Barack Obama has said it increases UK power and security to be part of the European Union, at a joint press conference with David Cameron.
Mr Cameron said being a member of the EU strengthened Britain’s “special relationship” with the US.
The US President earlier had lunch with the Queen with his wife Michelle at the start of a three day visit to the UK.
Mr Obama paid warm tribute to the Queen on her 90th birthday describing her as “truly one of my favourite people”.
Mr Obama’s intervention into the EU referendum debate has been criticised as “hypocritical” by London Mayor and EU leave campaigner Boris Johnson and UKIP leader Nigel Farage said he was the most anti-British US president ever.
The Duke and Duchess of Cambridge and Prince Harry will welcome the Obamas for dinner at Kensington Palace on Friday evening.
BBC deputy royal correspondent Sarah Campbell
The Duke of Edinburgh drove the Queen into the Castle grounds to meet the president and first lady as they disembarked from their helicopter.
After a quick chat, there was some discussion over where people should sit, with Mr Obama opting for the front seat.
Prince Philip, aged 94, returned to the wheel.
This is the third time the couples have met and the first time in the historic surrounds of Windsor Castle.
Their last meeting was during a visit in 2011 when the Obamas stayed in Buckingham Palace.
In 2009, in what was taken to be a sign of a friendly relationship between the families, the first lady was photographed with her arm around the Queen’s waist.
In their meetings since, including today, there does seem to be a genuine warmth between the two families.
Today’s lunch is private. To the frustration of the many journalists covering this visit, whatever the Queen makes of the president’s views …read more
Source:: BBC UK