The migrant crisis, with the number of people fleeing the volatile Middle East for Europe increasing every day, has been described as the largest exodus of people since World War II.
The image of a Syrian child found dead on a Turkish beach on the front pages of UK newspapers today led to a petition with over 100,000 signatures, which means the government would now have to debate the issue in Parliament.
"Britain is a moral nation and we will fulfil our moral responsibilities," Cameron said, though he refused to commit to any number of migrants the country would allow in.
The migrants are believed to be mostly from Syria but also from Iraq, Pakistan and Afghanistan.
UN special representative on international migration Peter Sutherland said that while some countries were "massively bearing the burden" of the migration crisis, the UK was among those that could do more.
Labour party leadership contender Andy Burnham called for Parliament to debate if the UK should take in more refugees when Parliament returns next week. Yvette Cooper, shadow home secretary, suggested the UK could take 10,000 Syrian refugees.
Attacking the government's response to the crisis so far, Scottish First Minister Nicola Sturgeon pledged that Scotland would "stand ready to offer sanctuary to refugees that need our help".
She said she was "reduced to tears" at the image of the dead child. "He and thousands like him whose lives are at risk is not someone else's responsibly; they are the responsibility of all of us.
UK Chancellor George Osborne said he was "very distressed" to see the image of a young Syrian boy lying dead on a beach in Turkey, but insisted there was no "simple answer" to the migrant crisis.
He said Britain would continue to take in "genuine refugees" with the situation kept "under review".
