Kim Leadbeater wrote to Justin Welby after he intervened in the debate over assisted dying, saying 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.
She proposed a meeting to discuss the issues. Lambeth Palace said it was trying to find a mutually convenient date.
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 was 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.
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