Foreign Office minister Alistair Burt warned the worsening civil war would attract jihadists to the country to fill the void created by fierce battles between Assad's forces and rebels.
He would not confirm claims from a British war photographer held hostage in Syria that 30% of his captors were British jihadists.
Mr Burt said: “It must be true to say that since the initial pressure and opposition against the Assad regime, which was local, the fight has been joined by others.
“The longer it goes on, without that ceasefire and political discussion, the worse that will get.”
Meanwhile, fighting in Aleppo entered its 11th day amid growing international condemnation of the Syrian government's crackdown on rebels fighting to hold the city.
Activists reported renewed bombardments of rebel-held neighbourhoods and clashes in many parts of Syria's largest city as the army pushed on with its offensive to retake the key northern city.
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