Chancellor George Osborne has said there must be a "comprehensive plan" to deal with the root causes of the Syrian refugee crisis which has seen hundreds of thousands of desperate people trying to seek sanctuary in Europe.
Mr Osborne said the problem had to be dealt with "at source", which meant tackling both the "evil" regime of Syrian president Bashar al-Assad and the militant jihadists of Islamic State (IS).
His comments came as some senior Tories called on the Government to bring forward plans to extend RAF air strikes against IS - also referred to as Isis or Isil - into Syria.
Former defence secretary Liam Fox said ministers should also seek to build international support for the creation of a safe haven inside Syria where refugees could be protected without attempting the hazardous journey to Europe.
On Friday, David Cameron bowed to intense public and political pressure, with the announcement that Britain would accept "thousands more" refugees from the camps in countries bordering Syria.
However, speaking to reporters at a meeting of G20 finance ministers in Turkey, Mr Osborne said that resettling refugees could only be one element of a wider plan to deal with the crisis.
"You have got to deal with the problem at source which is this evil Assad regime and the Isil terrorists," he said.
"You need a comprehensive plan for a more stable, peaceful Syria - a huge challenge of course, but we can't just let that crisis fester. We have got to get engaged in that.
"There are lots of things that we need to do and it is only by doing them all that you have a solution to this great, great challenge."
Dr Fox said that ministers should now be prepared to extend RAF strikes against IS in Iraq into Syria, as well as seeking support for an international safe haven protected by a no-fly zone.
"The policy of attacking Isis in Iraq but not in Syria is patently absurd which not only makes us less effective militarily but diminishes us in the eyes of other partners in the coalition," he said.
"Hand-wringing about the tragedy of the refugees is not enough. It is time that action was taken to deal with the root of the problem."
Some senior figures at Westminster have however expressed doubts as to whether Mr Cameron would be prepared to risk another Commons vote on military action in Syria after his bruising defeat on air strikes against Assad two years ago.
The Prime Minister has repeatedly said that he would seek a parliamentary consensus before attacking IS in Syria, and with the prospect of a victory for left winger Jeremy Corbyn in the Labour leadership contest, that would appear increasingly unlikely.
Meanwhile the Local Government Association is warning Mr Cameron that he must make resources available to support essential public services if Britain is to open its doors to a new influx of Syrian refugees.
David Simmonds of the LGA's asylum, refugee and migrant task force said councils were already spending significant sums supporting refugees at a time when services were under pressure.
"If we are going to scale those numbers up significantly we need to make sure that those kinds of resources are available to England's councils and also other public services to make sure that we have what is required in terms of school places, hospital beds, GPs that sort of thing," he told the BBC Radio 4 Today programme.