"Britain is not going to be playing a lesser role in the world," Cameron said as he arrived for a NATO summit in Warsaw dominated by concerns over Britain's post-EU future.
"We are not turning our back on NATO," he said, and Britain would discuss doing even more with its partners in the US-led alliance to meet changing security challenges.
Britain is a key nuclear-armed NATO ally, wields a permanent veto on the UN Security Council and enjoys a "special relationship" with the United States.
Obama insisted earlier today that the outcome would not undermine Britain's role in NATO but urged London and Brussels to avoid "protracted, adversarial negotiations" over their divorce.
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