Two new Health ministers have called for an overhaul of the law on assisted suicide.
Anna Soubry, a Tory promoted in last week's reshuffle, said the legislation needed to "evolve".
Liberal Democrat Norman Lamb said that while the issue is one of "personal conscience", "there is quite a strong case now for a discussion about a reform".
It comes after Tony Nicklinson, who had locked-in syndrome, died days after losing a legal fight for a doctor to help to end his life.
Ms Soubry told The Times: "I think it's ridiculous and appalling that people have to go abroad to end their life instead of being able to end their life at home. The rules that we have about who we don't prosecute allow things to happen, but there's a good argument that we should be a bit more honest about it."
Assisted suicide carries a sentence of up to 14 years.