The architect of a parliamentary bill to legalise assisted dying has invited the archbishop of Canterbury to meet her after he described a change in the law as dangerous.

Kim Leadbeater’s letter follows Justin Welby’s intervention in the debate over assisted dying, in which he said the MP’s private member’s bill would lead to a “slippery slope”, including a broadening of criteria and pressure on people to die prematurely.

The terminally ill adults (end of life) bill was formally introduced in the House of Commons on Wednesday and will be debated on 29 November. MPs are to be given a free vote on the emotionally charged issue, meaning they can vote according to their conscience.

Welby’s intervention is a sign of a potentially fractious national debate on end-of-life care over the coming weeks and months. In her letter, Leadbeater stressed the need to avoid “discord and division” in the debate about assisted dying.

Responding to Welby’s comments, she wrote: “We both value life unequivocally and I believe it is entirely possible to share that fundamental position while holding different views on whether the law should change to give dying people more autonomy and choice over how their lives end when that end is already very near.”

The archbishop’s concerns about a slippery slope were unfounded, she wrote: “If my bill is passed, parliament will have drawn a very clear and settled line that should not be crossed. We have ample evidence from overseas that this can be done.”

In response to Welby’s assertion that the medical profession opposed assisted dying, Leadbeater said she had recently met representatives of the British Medical Association “who were clear they no longer oppose a change in the law after a survey of doctors prompted them to adopt a position of neutrality”.

She wrote: “My proposed legislation is less about ending life, but very much about easing suffering and shortening death. The status quo simply fails to offer meaningful protection to dying people and their loved ones. My bill will introduce clarity, oversight, monitoring and regulation to practices that are already happening in the shadows.”

Leadbeater pointed out there was “diversity of thought within the Church of England as there is among people of other faiths”. She said she had spoken to many Christians who “feel the law as it stands can compromise a dying person’s ability to come to the end of a full and rich life with the same values with which they have lived, including love and compassion”.

She said she was sorry to hear about the circumstances of the death of Welby’s mother last year at the age of 93. Welby told the BBC his mother had described feeling like a burden. She also paid tribute to Welby’s “moral leadership” in the aftermath of the murder of her sister, the MP Jo Cox, saying it had been a great comfort to her family.

She wrote: “I do not claim this is a simple matter, or that it is possible to achieve a complete consensus on an issue that understandably prompts such strong feelings. But nor do I accept that such an important decision about how we reduce suffering at the end of life should sow discord and division. I do not want this debate to be conducted in a way that creates wounds we might struggle to heal in the future and I’m sure you agree.”

Lambeth Palace has been approached for comment.