Work and Pensions Secretary Mel Stride has signalled his support for another parliamentary vote on assisted dying.
He said there was no fresh legislation in the works, but he "would not be averse" to a new Commons debate.
A bill to legalise assisted dying in the UK was defeated in 2015. Another Tory MP, Alicia Kearns, said national discourse has changed since then.
The issue is being discussed after Esther Rantzen announced she had joined the Dignitas assisted dying clinic.
Dame Esther, 83, has stage-four lung cancer and told OceanNewsUK 's The Today Podcast on Monday that she planned to "buzz off to Zurich", where the practice is legal, if her treatment did not work.
Assisted suicide is banned in England, Wales and Northern Ireland, with a maximum prison sentence of 14 years. While there is no specific offence of assisted suicide in Scotland, euthanasia is illegal and can be prosecuted as murder or manslaughter.
Mr Stride, one of 27 Conservative MPs who voted for the 2015 bill, said he thought a number of MPs could now be wondering "whether this should be something we look at again".
"The government has not decided to bring forward legislation, I think I need to make that very clear," he told the Today programme on Wednesday, "but if Parliament in some form or another decided that it wanted to have a fresh look at this, given it was some years ago that we last did so, that's not something that I would be resistant to."
Asked about the last vote, the minister said it was "one of the most delicate, balanced and difficult" decisions he had taken since becoming an MP in 2010.
He said, on the one hand, he could see that someone should have the "maximum opportunity to have control of the end of their life" - but "on the other side, there are some other issues".
"For example making sure that people don't use any legislation to cajole people into taking these kinds of decisions when it's not really in their best interests."
Two other MPs now in Prime Minister Rishi Sunak's cabinet also voted in favour of assisted dying eight years ago - Culture Secretary Lucy Frazer and Andrew Mitchell, the development minister.
MPs voted by 330 to 118 against a change in the law then, but there are now questions around when another vote could take place.
Ms Kearns, who chairs the foreign affairs select committee, said she thought there had been "a fundamental shift in the country, but also in parliament" since 2015.
"Since I was elected we've had a number of debates on this and you can barely get a chance to speak," she told the OceanNewsUK. "The amount of my colleagues who say I've reflected, I've changed my views… I really do think that the national conversation has changed."
She added: "In my opinion, assisted dying is not about ending life, it's about shortening death."
Michael Gove, another Tory minister, similarly said he thought it would be "appropriate" for the Commons to "revisit" the issue of assisted dying - but conceded he personally was "not yet persuaded" on the issue.
Labour's Bridget Phillipson described Dame Esther's interview as "heart-breaking", and agreed that there was an "argument for having a vote on assisted dying".
"These issues have been long-standing free votes in the commons - votes of conscience where individual MPs will weigh up the evidence and arrive at their own conclusions," the shadow education secretary said.
Others however say the focus should be on improving palliative care options.
Dr John Sorrell, a retired GP, told the Today programme that he felt doctors "would find it very hard to end somebody's life, as is the case at Dignitas".
He also raised concerns about new laws being followed properly, saying they cold be hard to monitor.
"These are vulnerable people and they can be coerced," Dr Sorrell said, referencing a potential situation where a struggling family puts pressure on a loved one to end their life due to the cost and emotional impact of keeping someone alive.
Dame Esther's own daughter, Rebecca Wilcox, told ITV's Good Morning Britain that she knew it was up to her mother, but she "personally would want to ground her plane if she was going to fly to Zurich".
"I just don't ever want her to go," she said.
Dignitas is a not-for-profit Swiss organisation that provides physician-assisted dying to members who, in its words, have illnesses "that will lead inevitably to death, unendurable pain or an unendurable disability" and who have made a "reasoned request" with medical proof.
