Key said he personally supported euthanasia. He would not take the step himself, but he believed others should be able to.
However, there was strong opposition to it within the National caucus, he said.
Senior members of the Cabinet such as Bill English and Gerry Brownlee have previously voted against bills that would have made euthanasia legal.
"Ultimately you're dealing with a really sensitive issue and I think the process is best handled through a member's bill, as I've said so often before," Key said.
The Prime Minister said the select committee's work was still useful because it would inform any debate if a private member's bill on the issue was drawn.
National Party MPs would have a conscience vote on any euthanasia-related legislation, he said.
Act Party leader David Seymour has a bill in the private member's ballot, which would legalise voluntary euthanasia in New Zealand.
Leader Andrew Little said the Government should "at least" allow a euthanasia bill to come before the House so a debate could take place.
However, he said a law change would not be a priority for a Labour-led Government.
He would personally support the legalisation of euthanasia if it had the same safeguards as former MP Maryan Street's proposed bill.
Street's bill was withdrawn from the member's ballot ahead of the 2014 election at the request of former Labour leader David Shearer, who was concerned it could become a distraction in election year.
It was taken over by another Labour MP, Iain Lees-Galloway, but Little asked him not to return it to the ballot.
The Labour Party passed a remit at its annual conference on the weekend that said MPs would have a conscience vote on any euthanasia legislation.
Little said he was unsure about the level of support for a law change within his party.