Gordon Brown has paid tribute to the "great integrity" and "dedication" of the Archbishop of Canterbury, Dr Rowan Williams.
It comes as the embattled Anglican leader prepares to defend himself over his comments on sharia law.
Mr Brown's spokesman said the Prime Minister understood the "difficulty" currently facing Dr Williams. The two men had a "close" relationship and stay in close touch, he said.
The spokesman added: "The Prime Minister believes the Archbishop of Canterbury is a man of great integrity and dedication to public and community service and he understands the difficulty he is facing at the moment.
"The Archbishop has been clarifying and setting in a wider context the comments he has made and I'm sure he will continue to do so in the future."
But he went on: "The Prime Minister is very clear that British laws must be based on British values and that religious law, while respecting other cultures, should be subservient to British criminal and civil law."
The remarks from Downing Street come as Dr Williams faces a crucial test when he gives his presidential address at the opening of the General Synod, the Church's ruling body, in central London.
The Archbishop is expected to defend himself after a storm of hostile criticism following a BBC interview he gave last week in which he said the adoption of some aspects of Islamic sharia law in the UK "seems unavoidable".
The interview preceded a public lecture in which Dr Williams said UK law needs to continue to find accommodation with religious legal codes such as the Islamic system of Sharia law if community cohesion and development are to be achieved.
His remarks draw criticism from church leaders, secular groups and government figures with at least two Synod members calling for him to go.
Both these men are twin cancers that have been inflicted upon this once-great nation by Adolf Blair and need to be 'cured'.