Energy Secretary Ed Miliband also repeated that the law is “cruel” as it stands, saying he intends to back the Bill.
Disabled People Against Cuts co-founder Linda Burnip, however, warned: “Given how much Rachel Reeves could save with more and faster deaths of disabled people this prospect is particularly frightening for anyone disabled.
“I think it is also fair to say that until we all have a right to live – rather than just exist on some of the lowest benefit levels in Europe – we don’t want a right to die.
“For older people, we’ve seen how those over 65 years of age are frequently refused treatments that might either cure them, or at least prolong their lives.”
Care Not Killing chief executive Dr Gordon Macdonald said the Bill’s introduction was “clearly disappointing news.”
He said: “I would strongly urge the government to focus on fixing our broken palliative care system that sees up to one in four Brits who would benefit from this type of care being unable to access it, rather than discussing again this dangerous and ideological policy.”
Liberal Democrat leader Sir Ed Davey confirmed he would be voting against the Bill, drawing on his experience of looking after his terminally ill mother as a teenager, saying he would rather see improvements to end-of-life care.
“I think if people knew that the palliative care was better, many of them wouldn’t support this legislation,” he said.
Ms Leadbeater’s Bill would cover England and Wales only.
It will be the first time the topic has been debated in the House of Commons since 2015, when an assisted dying Bill was defeated.
Assisting someone to end their life is not a specific criminal offence in Scotland.