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."
HMS Bulwark has begun a rescue mission to save at least 500 migrants found in four boats in the seas off Libya.
"From first light this morning, a Merlin helicopter from 814 Squadron onboard HMS Bulwark has been conducting surveillance operations and has identified four migrant vessels in distress, containing a total of at least 500 people," a Ministry of Defence spokeswoman said.
"HMS Bulwark has now commenced rescue operations to recover those in the vessels."
It is estimated that more than 1,600 people have drowned so far this year trying to make the crossing.
Royal Navy warship HMS Bulwark is involved in a rescue mission to save at least 500 migrants found in four boats off the coast of Libya, the Ministry of Defence has said.
Royal Navy ship HMS Bulwark has already helped save the lives of more than 4,000 migrants - and tonight it will rescue more.
There are reports another 3,000 migrants have left Libya today, many on boats which are unseaworthy and do not even have engines.
After being towed out to sea, they are left to drift for days by human traffickers.
Defence Secretary Michael Fallon, who is aboard the ship tonight, told ITV News Europe is still not doing enough to tackle the problem.
He said: "The whole of Europe really need to adopt a more comprehensive approach to get after the traffickers, to understand how they're making money out of this trade in human misery and to do more to discourage people from leaving these countries."
Political correspondent Carl Dinnen reports from HMS Bulwark:
A British Navy warship has rescued 747 migrants trying to make the treacherous journey across the Mediterranean and delivered them to safety in Italy.
HMS Bulwark saved the migrants from dangerously overcrowded boats in the waters just north of Libya.
Many young children, some without parents, were among those rescued by crew aboard the ship.
ITV News Political Correspondent Carl Dinnen reports on their journey:
Hundreds of migrants fleeing war and poverty in Africa have been put ashore in Italy after a British navy ship rescued them from the Mediterranean. More than 700 people - including many children - were rescued by the crew of HMS Bulwark after their boat began to sink off Libya.
Hundreds of migrants - including 50 young children - have been rescued from an "unstable" ship in the Mediterranean sea near Libya, thanks to UK ship HMS Bulwark.
The double-decker, wooden-hulled boat was described by the Ministry of Defence as "heavily overcrowded", with 369 people packed on board.
As part of the international migrant search and rescue mission - codenamed Operation WEALD - Bulwark dispatched five of its specialised landing craft to rescue the migrants and bring them to safety.
All eight of its landing craft have been converted into rescue boats, piled high with lifejackets, medical equipment and emergency supplies.
The rescue was one of five which took place in the Mediterranean today, with Italian, Greek and Irish naval units all involved in saving some 800 lives. They will now be transferred to a dedicated port of safety.
Defence Secretary Michael Fallon welcomed news of the operation, but called for a better solution from UK and overseas governments.
HMS Bulwark and her crew have once again saved hundreds of lives in the Mediterranean migrant crisis, offering medical assistance, food, water and dry clothes to those in need.
A wider political solution is required to this crisis, but that does not detract from today’s rescue at sea.