Brown challenged by right-to-die campaigner Debbie Purdy
The exchange came at a pre-General Election question and answer session in Leeds, organised by the Yorkshire Post. A two-page report appears in Thursday's Yorkshire Post, with video coverage on this site.
Ms Purdy, who suffers from multiple sclerosis, won a landmark legal victory last year that forced the Director of Public Prosecutions (DPP) to spell out the circumstances in which relatives would be charged for helping someone to die.
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Hide AdShe welcomed the guidance for giving her clarity that husband Omar Puente would face prosecution for being present at her death.
But she urged the Prime Minister to go further and actually change the law. "Can we, the electorate, trust politicians that we elect to seriously consider the experience of jurisdictions where assisted dying is legal - to consider how to implement that in this country?" she said.
Mr Brown praised Ms Purdy as a "very brave person and a very brave campaigner", and said he understood "the difficulties of families that are placed in this most impossible of positions when people are suffering and they want to do something".
But he insisted that his personal experience with family members had convinced him that the law must stand.
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Hide AdHe pointed out that Cicely Saunders, who founded the hospice movement, had supported the ban on assisted suicide.
"I hope you will find, even though you disagree with me, that the DPP advice is helpful," he said. "But I hope you will also understand that these are very strongly held arguments on all sides, including by people of different faiths.
"I really want to support the interpretation of the DPP, but I would not support myself a change in the law at the moment."