LONDON, Sept 3 (Reuters) - Prime Minister David Cameron said on Thursday that Britain would stick to its present course on the issue of Syrian refugees, resisting calls to announce a sharp increase in the numbers to be given sanctuary in Britain.

Amid a public outpouring of emotion over the widely published image of a dead Syrian toddler washed up on a Turkish beach, Cameron said he was "deeply moved" by the picture and that Britain would fulfil its moral responsibilities.

"We are taking thousands of Syrian refugees and will continue to do that. As I said yesterday, we keep that under review," Cameron said in televised comments.

"But ... there isn't a solution to this problem that's simply about taking people," he added, calling for comprehensive solutions to the problems in Syria and Libya, and for action against Islamic State and people-trafficking gangs.

(Reporting by Estelle Shirbon) ((estelle.shirbon@thomsonreuters.com; +44 207 542 1346;))