Parliament should not wait for a private member's bill to be drawn from the ballot, he said.
"This debate needs to happen now. Prime Minister, I urge you to give the public what they want and start the debate. I urge you to follow my wife's example and to be a courageous leader ... let us give Lecretia her legacy."
Last night, Mr Key - who has previously voted for a failed euthanasia bill in 2003 - extended his sympathies to Ms Seales' family.
However, he reiterated National's position that the issue would be best dealt with by a member's bill.
"The matter of assisted suicide is a conscience issue and therefore would be dealt with by a conscience vote," Mr Key said in a statement.
But Opposition parties yesterday signalled a new approach to have the issue examined by Parliament as soon as possible.
Labour leader Andrew Little is backing a plan by his MP Iain Lees-Galloway to table a petition by the End of Life Choice Society to Parliament later this month, in the hope it will lead to a full inquiry by the select committee that considers it.
"Lecretia's bravery has created the public conversation that has given MPs the confidence they need to address this issue," Mr Lees-Galloway said.
"Our view is that [tabling the petition] should trigger a wide-ranging inquiry into the issues of end-of-life choice, so that Parliament can progress it with a bipartisan approach."
Such an inquiry would need the agreement of the majority of MPs on a select committee to initiate. The 10-person justice committee has five National MPs.
Mr Lees-Galloway took on a private member's bill by former Labour MP Maryan Street after the last election, but was told by Mr Little last December to drop it.
That order had been criticised, Mr Little said yesterday, but he felt the new approach by Mr Lees-Galloway was better. Mr Little said he personally believed the law did need to change, but only with strong safeguards.
Greens justice spokesman David Clendon said his party would support Labour's efforts to get the issue before select committee.
"Clearly there is a public interest, and a public conversation would be a good thing."
Ms Seales, a 42-year-old Wellington lawyer, died yesterday morning before the decision of Justice David Collins was released publicly, but was disappointed that the High Court judge ruled her doctor could not administer a fatal dose of drugs without risk of criminal prosecution.
The judge said the "complex legal, philosophical, moral and clinical issues raised by Ms Seales' proceedings can only be addressed by Parliament" and the fact that three private members' bills had previously failed did not give him a "licence" to intervene.
At a media conference yesterday, Mr Vickers spoke of telling his wife of the judgment on Tuesday night.
"Lecretia listened to me as I explained the decision. Even though she couldn't speak, she was able to share her feelings through her expression. There was no mistaking her response.
"She was hurt and disappointed. She fixed me with a stare with her good eye as if to say, 'Isn't this my body? My life?'
"Her breath slowed and she turned her head away. Her reaction utterly broke my heart."
Regardless of the result of the ruling, Ms Seales previously told the Weekend Herald she would be proud if her court case prompted wider legislative change.
"I'm reasonably confident that I won't be able to see it through to the end. But if I can get it started, that would make me happy."
Past attempts
• A private members' bill by former Labour MP Maryan Street failed to be selected for 18 months before being withdrawn late in 2013 after a lack of support from her colleagues. The End of Life Choice Bill would have allowed certain New Zealand residents aged 18 or over, such as those with a terminal disease or physical or mental condition that makes life unbearable, to have assistance to die.
• Former NZ First MP Peter Brown's "Death with Dignity" bill was narrowly defeated in a conscience vote 60-58 in its first reading in 2003. Prime Minister John Key voted for that bill, as did current MPs Murray McCully, Maurice Williamson, David Cunliffe, Ruth Dyson, Phil Goff, Winston Peters, Pita Paraone and Metiria Turei. A previous bill, championed by Michael Laws in 1995, failed by 61 votes to 29.