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The crew of Royal Navy vessel HMS Bulwark expects to have rescued more than 1,000 migrants by the end of today.
ITV News' Carl Dinnen reports that 378 people were rescued from just one wooden boat this morning in the sea off Libya.
The crew have also rescued people from six inflatable boats and a seventh that was picked up by the Italian Coast Guard.
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:
Latest ITV News reports
Hundreds of migrants were rescued from the Mediterranean at the weekend - but their journey will not stop there, as they tell ITV News.
Britain's flagship HMS Bulwark has been involved in its "largest operation to date", plucking more than 1,000 migrants from makeshift boats