The Right Reverend Mark Davies gave his message at Lourdes in France to 800 pilgrims.
He has called on the community to lobby MPs, focussing on a private members bill being introduced by Wolverhampton Labour MP Rob Marris in September.
Bishop Davies says the bill would amount to "the medical killing of some of the weakest members of society."
He also stressed there is a danger that legalising assisted dying could lead to people coming under pressure to end their lives if they begin to see themselves as a burden to others: "We have good reason to fear that the right to die will quickly become the duty to die.
"And those who should be most cherished and cared for will increasingly see themselves as an unwanted burden to society."
Bishop Davies said that the proposed law will "remove legal protections for the lives of some of the most vulnerable in our land.
"It is the first step on the road to euthanasia: the medical killing of some of the weakest members of society," he said in The Shropshire Star.
He added: "By the proposed law, those in our hospitals and care homes will be offered assistance to commit suicide.
"The very ones who should be accorded the greatest support will be legally offered help towards killing themselves.
"Conscious of the sometimes scandalous neglect of elderly people in our present health and care provision we can imagine the pressures under which some of the most vulnerable will come if assisted suicide becomes the mindset of British society."
The bill will be debated in Parliament on 11th September.
Bishop Davies said he is worried that: "We may only have a matter of weeks to make our voices heard before Parliament decides whether a culture of care or a culture of suicide and eventually of killing prevails."
The idea behind the bill is to allow the opportunity for terminally ill people to choose to be assisted to die to end their lives if they so wish.
If passed, it would mean those with less than six months to live, who are of sound mind and a have made this choice, would be allowed to ask for a lethal prescription of drugs.
An additional two doctors would have to agree with the patients decision and their decision would be reviewed by a High Court judge in each case.
The bill does not differ from a previous bill proposed to the House of Lords by Lord Falconer last year, but it adds the requirement for a High Court judge to approve applications for suicide within a fortnight of them being made.
