Conservative leader David Cameron has rejected any expansion of Sharia law in the UK, saying it would undermine society and alienate other communities.
Mr Cameron said state multiculturalism had disastrous results
In a speech in London he said allowing two laws to work side by side would be dangerous adding: "All citizens are equal before the law."
He also said "state multiculturalism" had produced "disastrous results".
It follows comments by the Archbishop of Canterbury that adopting parts of Sharia law in the UK was unavoidable.
Dr Rowan Williams came under heavy pressure from traditionalists to apologise for the suggestion and has since insisted he was not advocating a parallel set of laws.
The archbishop said some remarks had been taken out of context and that what he meant was similar to Catholic agencies having special opt-outs on gay adoption.
In his speech on "extremism, individual rights and the rule of law", Mr Cameron said British law already allowed individuals to settle private disputes in different ways - but under the ultimate jurisdiction of English law.
He added: "If the archbishop was not talking about the status quo - about what already exists - the danger is that he was actually suggesting else - something more akin to different laws for different communities.
"This would be dangerous and illiberal. It would be dangerous because in Britain, all citizens are equal before the law. That concept is absolutely fundamental to our democracy - itself developed and nurtured over centuries. "
In his first formal public comments on the row earlier this month he said an introduction of Sharia law for Muslims "wouldn't strengthen our society - it would undermine it".
He said it would alienate others not subject to "preferential treatment", demoralise Muslims who embrace liberal values and would provide "succour" to separatists.
Mr Cameron also criticised what he called "state multiculturalism" saying it allowed and encouraged people to "live separate lives, apart from each other and apart from the mainstream".
"I believe that state multiculturalism is a wrong-headed doctrine that has had disastrous results.
"It has fostered difference between communities and it has stopped us from strengthening our collective identity. Indeed it has deliberately weakened it."
He said any expansion of Sharia law was the "logical endpoint of the now discredited doctrine of state multiculturalism, seeing people merely as followers of certain religions, rather than individuals in their own right within a common community".
It was not just the Conservative Party that wanted to move away from state multiculturalism - it was becoming the consensus view, he suggested - as seen in citizenship ceremonies introduced by the former Labour home secretary David Blunkett.