Labelling of meat products with information about religious slaughter techniques is a matter between retailers and restaurants and their customers, Downing Street has said.
David Cameron's official spokesman signalled that the Prime Minister does not believe the Government needs to intervene in the current row over labelling of halal and kosher products.
Representatives of Jewish and Muslim groups have written a joint letter calling for consumers to be given detailed information about slaughter methods when buying meat, following a string of press stories revealing that halal meat is routinely sold in the UK without buyers being told.
A majority of New Zealand lamb sold in UK supermarkets comes from halal abattoirs, while restaurant chains including Pizza Express use meat from chickens slaughtered in accordance with halal procedures.
A significant proportion of meat produced by exporting countries such as New Zealand is slaughtered to halal standards, in order to ensure it can be sold to both Muslim and non-Muslim nations.
Asked whether Mr Cameron thought the Government should act to ensure halal and kosher meat is clearly labelled, the PM's spokesman said: "The Prime Minister's view is that it is an issue of consumer choice and consumer information.
"So it is a matter for retailers and restaurants to work with customers and consumer groups and representatives of faith organisations.
"He is a strong supporter of religious freedoms, including religious slaughter practices."
The spokesman said that Mr Cameron had visited a slaughterhouse in his Oxfordshire constituency where meat is prepared according to the traditional Jewish shechita practices. He added: "I don't think the PM has concerns about the meat that he buys. He very much understands why some people have concerns about the information they are getting."
Asked whether Mr Cameron thought consumers should ask about the slaughter methods used for the meat they buy, the spokesman replied: "Many consumers will rightly be very demanding of their retailers, the places they shop and the places they go out to eat. I am not telling shoppers or people who go to restaurants what they should do."
He added: "The Prime Minister's view is that the approach we currently have is absolutely the right one."
In a letter to the Daily Telegraph, the chairman of Schechita UK, Henry Grunwald, and the deputy secretary general of the Muslim Council of Britain, Shuja Shafi, called for all meat to be labelled to indicate slaughter methods.
"Consumers should be informed whether an animal has been mechanically stunned prior to slaughter and whether it has endured repeat stuns if the first attempt was ineffective," wrote Mr Grunwald and Dr Shafi. "They should also be told the method of slaughter: captive bolt shooting, gassing, electrocution, drowning, trapping, clubbing or any of the other approved methods.
"Comprehensive labelling should be supported by faith communities and animal welfare groups alike. It would offer all consumers genuine choice, whether they are motivated by animal welfare, religious observance, or even intolerance of anyone who looks or worships differently to them."
Andrew Opie, director of food and sustainability at the British Retail Consortium, said: "British retailers know that animal welfare standards are a key issue for their consumers. All own-brand meat from major UK supermarkets comes from animals that have been stunned before they are killed and all our members have confirmed all their own-brand fresh meat is from animals that have been pre-stunned before slaughter.
"However, we understand there are some customers who want meat from animals that have been slaughtered in accordance with strict religious protocols and in relevant stores meat produced by specialist producers is available with clear certification that is branded halal and kosher certified meat produced by specialist companies.
"There appears to be some confusion over meat that may be produced for a potential halal market but is sold as own-brand, but all those animals are stunned prior to slaughter. As the overwhelming majority of meat sold in UK supermarkets is own-brand and from animals that have been stunned prior to slaughter, we do not see the requirement to separately label meat based on the method of slaughter."
Philip Lymbery, chief executive of Compassion in World Farming, said: "Are we going to treat animals humanely or not? When animals are killed without stunning, the science shows that they suffer extreme pain, distress and anxiety.
"I have absolute respect for religious beliefs. As up to 90% of animals killed for halal purposes in Britain are already being slaughtered with pre-stunning, we should make it illegal across the board for animals to be slaughtered without pre-slaughter stunning.
"We are calling for all meat to be labelled according to slaughter method. In addition, the Government should have the courage to close the loophole that allows exemptions on pre-slaughter stunning for religious purposes."