"In some ways it should be beyond party politics," National MP Chris Bishop said.
A counter-demonstration of people opposed to euthanasia also gathered at Parliament.
Family First New Zealand director Bob McCoskrie said he was concerned the "right to die" would become a "duty to die" for vulnerable people including the elderly and disabled.
Lecretia Seales was unsuccessful in seeking a High Court ruling that would let her doctor help her die without criminal prosecution.
Ms Seales died of natural causes on June 5, shortly after her family and lawyers received the ruling.
Act's David Seymour, Green Party MP Kevin Hague, Labour's Iain Lees-Galloway and Chris Bishop of the National Party joined Labour MP Maryan Street in receiving the signatures on the steps of the Parliament Buildings.
Mr Vickers said Parliament had in previous years repeatedly had the "opportunity to grapple with the issue of end of life choice only to put it aside."
He said the petition reinforced the "clear public support" for lawmakers to address the issue.
"Through her case, Lecretia sought to provoke change and action but she knew that whatever the result of her case, it would and indeed should end up here," he said outside Parliament.
"She sacrificed some of her remaining time with me and her loved ones in pursuit of a more compassionate, merciful and free society -- and for more meaningful choices for those confronting terminal illnesses like her."
Carole Sweney, Voluntary Euthanasia Society national secretary, said her organisation spent about three months collecting the signatures.
Mr Lees-Galloway said the appearance of MPs from different parties showed the issue transcended partisan politics.
He praised Mr Vickers and Ms Seales for their efforts to put the issue of voluntary euthanasia in the spotlight.
"It will go down in history as one of the most important efforts to make New Zealand a better place to live..."
He said receiving the petition signatures was "a giant step forward for end-of-life choice."
Mr Hague said he wanted Parliament's health select committee to discuss the issue.
Mr Seymour said the issue was "deeply important" for New Zealand.
He said Mr Vickers showed admirable strength in advancing the debate on voluntary euthanasia.
"This issue is legally the right thing to do," he said. "This is ethically and morally the right thing to do."
Mr Seymour said Kiwis "overwhelmingly" wanted Parliament to address the issue.
Ms Street, who previously introduced the unsuccessful End of Life Choice Bill, said the new petition did not ask for a bill, although there was 'a perfectly serviceable" one available already.
"It asks for an inquiry into public opinion on the issue of assisted dying in certain circumstances -- terminal illness and irreversible conditions that make life unbearable."