Gordon Brown pledged that the Government would take "all the urgent action that is necessary" to halt the spread of swine flu.
Speaking in the Polish capital, Warsaw, the Prime Minister insisted that Britain was well-prepared to deal with a major flu outbreak.
He said he would be taking part in a meeting of the Government's Cobra emergencies committee being chaired by Health Secretary Alan Johnson.
"We have been preparing for this kind of scenario for many years. Britain is among the best prepared countries in the world," he told a joint news conference with Polish Prime Minister Donald Tusk.
"We, together with the World Health Organisation and our partners in Europe and internationally, will continue to take all the urgent action that is necessary to halt the spread of this virus."
Mr Brown acknowledged that there were public concerns about the outbreak following the confirmation on Monday of the first two cases in Britain.
He said the two people affected were now in "better health" and that one of them may be well enough to leave hospital shortly.
He urged anyone who suspected that they might be suffering from the disease to follow the advice of the NHS and to stay at home and call their GP or NHS Direct.
"I .....continued below
Advertisement starts
Advertisement ends
understand the very real concern that people across Britain, and indeed across Europe and the world, have about the outbreak of this swine flu disease," he said."We are all vigilant, we are all alert, we are all aware that people have fears about swine flu at the moment and we are aware that there is action that we can take and will take to make sure that those fears are allayed."
