Care minister Norman Lamb has backed moves to legalise "assisted dying".
The Liberal Democrat said he would vote in favour of allowing terminally ill adults with less than six months to live to choose to be helped to kill themselves.
Legislation has been drawn up by Labour former lord chancellor Lord Falconer of Thoroton and MPs would be allowed a free vote on the issue if it is debated in the House of Commons.
Several previous attempts to legislate on the issue have failed and both David Cameron and Nick Clegg have said they personally oppose such a change.
But Mr Lamb said that there appeared to be "quite widespread public support" for ending what was a "cruel" system that left relatives unsure if they would be prosecuted.
Assisted suicide remains a criminal offence in England and Wales, technically punishable by up to 14 years in prison.
Guidelines issued by the Director of Public Prosecutions in 2010 after one high-profile case indicated that anyone acting with compassion on the will of a dying person was unlikely to face criminal charges.
That has been the case in around 90 such deaths examined by prosecutors since then.
Critics - including doctors, disability campaigners and churches - warn that a formal change in the law would leave people vulnerable to pressure from family and others to end their lives.
The issue has split the House of Lords in recent debates, with the severely-disabled Baroness Campbell of Surbiton among those warning of the dangers.
"It is not only dangerous for those who may see suicide as their only option, it can also be tempting for those who would benefit from their action," she told peers.
Former Commons speaker Baroness Boothroyd insisted however that it was vital to change a system that added "cruelly to the suffering of people who want to die with dignity".
Mr Lamb said that his own conversations with terminally-ill patients had swung his opinion in favour of legalisation which included sufficient safeguards.
"What an invidious situation to leave people in," he told the Murnaghan programme on Sky News.
"Can we really be comfortable with a situation where people, acting out of compassion for a loved one who is dying, are left uncertain as to whether they will face prosecution?
"There need to be proper safeguards - that's critically important," he added.
"You have absolutely got to guard against relatives or others seeking to get control of the estate. We have to be certain that it is an individual decision.
"I think you can meet those safeguards."
Under Lord Falconer's proposals, two doctors would have to sign off the fatal dose.
Liberal Democrat activists have previously voted in favour of such legislation.
Mr Lamb sad it remained "v ery hard to judge" whether it would be supported in the Commons - with the Sunday Telegraph suggesting around a third of MPs are in favour, fewer opposed but 40% undecided.
No date has yet been set for Parliament to debate Lord Falconer's private member's bill.
MPs are traditionally freed from the constraints of party discipline on such issues and allowed to vote according to individual conscience.
Foreign Secretary William Hague warned about the dangers of creating a "grey area" but indicated that he remained opened to be persuaded to reverse his previous opposition.
"I am always very concerned... that we don't create some new grey area in the law that can be misused," he told the programme.
"So I have always erred on that side of the argument but there are very strong and legitimate arguments in both directions.
"In past years I have voted against these proposals but we'll see, I will look at it afresh, I will read the letters that come from my constituents and decide how to vote."
Shadow chief secretary to the Treasury Chris Leslie told the programme he was "not yet convinced that there is a need to change the law".
Richard Hawkes, chief executive of the disability charity Scope, said the present legal ban was a "crucial protection" and should not be dropped.
"The ban on assisted suicide sends a really powerful message countering the view that if you're disabled it's not worth being alive, and that you're a burden," he said.
"It provides crucial protection to any person who feels under pressure to end their life.
"There are loud, well-organised and influential calls to legalise assisted suicide for terminally ill adults.
"But we hope politicians will decide against changing a law that works on the basis of a few powerful, but exceptional cases."
He said the debate " tells us a lot about attitudes to disability.
"Why is it when someone who is not disabled wants to commit suicide we try to talk them out of it, but when a disabled person wants to commit suicide we focus on how we can make that possible?"
A spokesman for the Care Not Killing alliance said: "There is nothing liberal about wanting to end the lives of the terminally ill, the disabled and the elderly.
"What we should be discussing is how we ensure equal access to good quality medical care and life-saving and preserving drugs r ather than once again debating a law that has been discussed and voted on numerous times since 2006.
"We would be delighted to meet with Mr Lamb and members of the medical and disability communities to explain to him why we are firmly opposed to changing the law."
A Ministry of Justice spokeswoman said: "The Government believes that any change to the law in this emotive and contentious area is an issue of individual conscience and a matter for Parliament to decide rather than Government policy."