David Cameron has agreed upon the need to "maintain momentum" in the international fight against so-called Islamic State (IS) as Barack Obama said he would send 250 more American troops to Syria and urged allies to increase their efforts.
The US president made the announcement as he ended a trip to the Middle East and Europe with a meeting in Germany of the G5 powers to discuss the response to a series of global threats.
German chancellor Angela Merkel, French president Francois Hollande and Italian prime minster Matteo Renzi joined the Prime Minister and the US president in Hanover for the mini-summit.
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Mr Obama - who has previously railed against "free riders" among America's allies on security - warned that Europe had sometimes been "complacent about its own defence".
He is committing another 250 special operations forces to Syria to counter the spread of IS - also known as Isis, Isil and Daesh.
A Downing Street spokesman said the leaders had "agreed on the need to maintain momentum and continue coalition efforts to defeat and degrade Daesh in both Syria and Iraq, including through online counter-extremism activity".
They also agreed on the need to give "full support" to the new Government of National Accord in Libya, with the PM said to have pressed over the need to help build the capacity of the Libyan coastguard to help stem the flow of illegal migration across the Mediterranean into Europe.
Other issues discussed included the EU's migration crisis deal with Turkey and Ukraine.
Mr Cameron also used to occasion to meet separately with Mrs Merkel and Mr Renzi, the spokesman said.
Former prime minister Tony Blair said there were "very powerful reasons of self interest for Europe - and I include Britain in that - to be stepping up to the plate in military terms" in the fight against IS, including in Libya.
He told CNN's Amanpour programme that the EU had to debate "how you pool defence capabilities to leverage their combined weight to make them far more effective" - though that would fall short of creating a European army.
The new US forces would make "a big difference", he said.
Military intervention in Libya was "necessary" to disrupt IS preparations for terror attacks in Europe and elsewhere, he said, pointing out there was "a far greater plethora of training camps and capabilities" than al Qaida had in the period before the September 11 atrocities in the US.
"If we are being vigilant about our own security and our own future then I don't think there is an option but to go and take these people on wherever they are."
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