The government has said it will review the labelling of halal meat if the food industry does not take action.
The prime minister's spokeswoman confirmed the government wants more "transparency" on the issue.
Five leading supermarkets say some of the meat they sell could qualify as halal but is not labelled as such.
They said animals are stunned before being killed and the only difference from standard meat is that they are blessed as they are killed.
On Thursday, Downing Street said that the labelling of ritually-slaughtered meat was a matter for retailers, customers and faith groups.
But the Downing Street spokeswoman said David Cameron thought British consumers wanted to understand more about how their meat was slaughtered.
The government would see if the process became more transparent and "review it in a few months' time", she said.
It is too early to say whether the review will include the compulsory labelling of products, she said.
Marks and Spencer, Tesco, Morrisons, Waitrose and the Co-op said their New Zealand lamb was halal, while Pizza Express has already revealed its chicken is killed according to Islamic tradition.
In each case, the retailers said the animals were stunned before they died.
According to the Halal Food Authority, stunning cannot be used to kill an animal, but it can be used if the animal survives and is then killed by halal methods.
Most animals slaughtered in the UK for halal meat were stunned before they died, according to research.
Faith leaders have also called for clearer information about slaughter methods.
In a joint letter to the Daily Telegraph, Henry Grunwald, chairman of Shechita UK, which represents the Jewish method of religious slaughter, and Dr Shuja Shafi, of the Muslim Council of Britain, wrote: "Comprehensive labelling should be supported by faith communities and animal welfare groups alike."