David Cameron is to set out his plan for tackling the crisis in Syria within days, in a bid to win support for air strikes against Islamic State fighters.
On Saturday, the prime minister welcomed a UN resolution asking nations to “combat by all means” the IS threat.
He is due to meet French President Francois Hollande in Paris on Monday.
In the wake of last week’s terror attacks in Paris, the leaders will discuss ways of co-operating on counter-terrorism and the fight against IS.
MPs voted against UK military action against Syrian President Bashar al-Assad’s government in 2013.
But they did later approve British air strikes against IS extremists in Iraq.
IS has claimed responsibility for the gun and suicide bomb attacks in the French capital on 13 November, which left 130 dead – as well as recent attacks in Tunisia, Egypt, Beirut and Turkey among others.
Commons vote on military action?
The prime minister has promised to set out a “full-spectrum” strategy, including military, counter-terrorism and humanitarian actions – following which, the BBC understands, there will be a push to convince MPs across the political spectrum to approve military action in Syria.
Mr Cameron has said he will only call a Commons vote on the issue if he can be confident he will win.
BBC political correspondent Iain Watson says the prime minister will set out a series of proposals towards the end of the week, but adds that the PM will be in no rush to bring about a vote.
Privately, some Labour shadow ministers say they are willing to support the prime minister rather than their own more cautious leader Jeremy Corbyn if a convincing case is made for air strikes as an element in a broader plan, our correspondent adds.
What does Labour leadership think?
In a speech on Saturday, Mr Corbyn, who is under pressure to allow his MPs a free vote on the issue, warned against “external intervention” in Syria.
The UN resolution, which was unanimously approved by 15 countries, should be used to bolster efforts to find a diplomatic solution to the conflict, he said.
His close ally, Shadow Chancellor John McDonnell, said if there had to be troops on the ground in Syria, they should come from the region itself.
“This isn’t a war like the Second World War, where you fight against an enemy in one terrain, you defeat them, they sign a peace treaty and that’s it,” he told the BBC.
The US and the UK getting involved in another war in the Middle East played into the IS “narrative of crusader invasion”, he said, and would also not defeat the group’s supporters “located in most of our capital cities”.
‘Price for not getting involved’
Meanwhile, Chancellor George Osborne said on Sunday it was “very easy to always count the cost of getting involved” in conflict overseas.
But if the UK had intervened earlier against the Assad government, the conflict may not have escalated to its current situation, he told the BBC.
“Now we’re seeing there is a price for not getting involved,” he said.
The SNP has said it is “is prepared to listen to the prime minister’s case on military intervention”.
But it said “as well as its legality, he must address the efficacy of military intervention and how it will contribute to a wider initiative to end civil war and secure reconstruction”.
The Democratic Unionist Party in Northern Ireland, which holds eight seats at Westminster, said it would back British military force in Syria provided it was “realistic and in the national interest”.