David Cameron is holding talks in Paris with French President Francois Hollande on co-operation in the fight against so-called Islamic State.
France is pushing for a stronger international coalition against IS.
The meeting is likely to help inform any new attempt by the prime minister to persuade Parliament to support RAF air strikes in Syria.
The meeting comes after IS claimed to have carried out the attacks on Paris, which left 130 people dead.
IS has also claimed recent attacks in Tunisia, Egypt, Beirut and Turkey among others.
BBC correspondent Kevin Connolly said that alongside the expected comparing of notes on security co-operation and intelligence sharing between Britain and France, the meeting will raise the question of the scope of British air operations against IS targets in the Middle East.
Currently, the RAF are only able to bomb such targets in Iraq, after MPs voted in 2013 to not allow bombings to take place in Syria.
But they did later approve British air strikes against IS extremists in Iraq.
Cameron may be expected to use what he hears from Hollande to help shape the British debate about whether to do more in the aftermath of the Paris attacks, our correspondent added.
Cameron is preparing to set out his plan for tackling the ongoing crisis in Syria this week, in a bid to win support for air strikes against IS fighters based there.
It comes after a Foreign Affairs Committee report said the UK should not join allied bombing in Syria without a coherent international strategy on IS.
Defence Secretary Michael Fallon, who is to brief Labour MPs next Wednesday, would not be drawn on when MPs would be asked to vote but said the UK's military capability - such as the use of Brimstone missiles - would be an important contribution to the international fight against extremists.
"We have to make our case," he told BBC Radio 4's Today.
"Understandably MPs want to be sure that there is a political track to this as well, that we are working with everyone in the region to create a more comprehensive, moderate government in Syria that will bring long-term security after the striking has finished.
"But we will also be setting out the moral case that we have French aircraft, American aircraft, Australian aircraft coming half way around the globe and we can't let them take all the burden and all the risk of fighting Islamic State on our behalf."
Shadow defence minister Maria Eagle told the BBC: "We don't know what the prime minister is going to come up with yet... as long as MPs can see a plan that's supported by all, there is a chance we can agree on a proper way forward."
She added: "We need to see the plan that the world comes up with will work before we decide how to vote and how the Labour party will whip its MPs."
The prime minister will appear in the House of Commons in the coming week to set out a "full-spectrum" strategy - including military, counter-terrorism and humanitarian actions.
On Friday, the UN Security Council unanimously adopted a resolution to "redouble" action against IS.
Meanwhile, Hollande will meet US President Barack Obama in the White House on Tuesday, to further discuss bolstering the international effort against IS.
The French president then goes to Russia for similar talks with President Vladimir Putin.