Britain is a country that "doesn't walk on by", David Cameron said as HMS Bulwark undertook another rescue mission off the coast of Libya.
Arriving at the G7 summit in Germany, the Prime Minister said the flagship had been deployed because Britain is a "country with a conscience".
"HMS Bulwark, the Royal Navy flagship, is in the Mediterranean because we want to save lives," Cameron said.
But he warned, "We need to deal with the causes of this migration, not simply with its consequences."
David Cameron is expected to call on leaders at the G7 summit to help eradicate global corruption in the wake of the Fifa scandal.
Speaking ahead of the gathering, he said, "Corruption is the cancer at the heart of so many challenges in our world".
"I'm putting it on the table here, and saying this is something we must not turn a blind eye to as perhaps was done for too long with the world of football."
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The Prime Minister has signalled that Britain could leave the European Convention on Human Rights after he insisted he ruled nothing out in achieving the Government's aims.
Mr Cameron told MPs gathered in the Commons for Prime Minister's Questions he wanted British judges making decisions in British courts, with the UK Parliament accountable to the people of the country.
He said: "We're very clear in what we want, which is British judges making decisions in British courts and also the British Parliament being accountable to the British people.
"Our plans set out in our manifesto do not involve us leaving the European Convention on Human Rights.
"But let's be absolutely clear: if we can't achieve what we need I rule out absolutely nothing in getting that done."
The Prime Minister has used a question from a Conservative Party backbencher to insist that the NHS will remain free at the point of use under his government.
During his first Prime Minister's Questions as leader of a majority Tory government, Mr Cameron also said that the health service will get an extra £8bn in extra annual funding.
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