The Archbishop of Canterbury and other Christian, Jewish, Muslim and Sikh leaders want politicians to reject proposals to permit doctors to prescribe a lethal dose to terminally-ill patients.
His predecessor, the former Archbishop of Canterbury, Lord Carey has argued in favour of a change in the law, despite the Church of England's official opposition to it.
The Private Member's Bill proposes legalising assisted suicide be debated on Friday in the House of Commons.
Currently, assisted suicide is illegal under the Suicide Act 1961 and is punishable by up to 14 years in prison.
Writing in the Observer newspaper, Most Revd Justin Welby said he and other faith leaders had spoken out because they believe changing the law would have "detrimental effects" on society.
"A change in the law to permit assisted suicide would cross a fundamental legal and ethical Rubicon," he said.
"This respect for the lives of others goes to the heart of both our criminal and human rights laws and ought not to be abandoned.
"While it is not a crime in the UK for someone to take his or her own life, we recognise that it is a tragedy and we, rightly, do all that we can to prevent suicide.
"The assisted dying bill requires us to turn this stance on its head, not merely legitimising suicide, but actively supporting it."
Mr Welby said asking to sanction doctors to take part in a person's bid to end their own life would be "a change of monumental proportions both in the law and in the role of doctors".
He added: "Once a law permitting assisted suicide is in place there can be no effective safeguard against this worry, never mind the much more insidious pressure that could come from a very small minority of unsupportive relatives who wish not to be burdened."
Among the faith leaders to sign the joint letter are Dr Shuja Shafi, secretary general of the Muslim Council of Britain, Ephraim Mirvis, chief rabbi of the United Hebrew Congregations of the Commonwealth and Lord Singh of Wimbledon, director of the Network of Sikh Organisations UK.
At least 35 Britons went to the Dignitas clinic in Switzerland to end their lives last year, campaign group Dignity in Dying said.
The latest Commons bid to give terminally-ill patients the right to die will be based on legislation championed by former lord chancellor, Lord Falconer of Thoroton, which ran out of time in the House of Lords.
