MacKay, who is not seeking re-election this October, said he suspects it is "very likely" the government — be it Conservative or otherwise — will need more time to address the decision, which came down in February.
In finding that Canada's prohibition on physician-assisted suicide was a violation of the Charter of Rights and Freedoms, the high court gave Parliament one year to deal with the issue in legislation.
The court said the response would have to recognize the right of clearly consenting adults who endure intolerable physical or mental suffering who wish to end their lives with a doctor's help.
MacKay said there is "no guarantee" the court would be willing to grant an extension, but he said it would be a "reasonable request." He also insisted the next government would address the issue because of the legal void it creates.
"To do otherwise, I think, would be dangerous and irresponsible," MacKay said as he vowed to launch formal consultations on the issue "very, very soon."
The government has already held informal discussions on the issue and is reviewing foreign precedents, he added. However, with Parliament poised to rise for the summer and a fall election on the calendar, time is short.
"Do we have sufficient time? Certainly not in the life of this Parliament," MacKay said.
"The legislative time frame to present a bill, to have it go through Parliament, and be seriously debated in Parliament at all its stages, I think would take us well beyond that February date."
Dr. Chris Simpson, the president of the Canadian Medical Association, said his organization would support extending the deadline in order to "get this right." But there are limits, Simpson said.
"I wouldn't want to see it be put off indefinitely," he said. "I think that is the worry."
Simpson said the CMA has started its own broad consultation process, which involves speaking to regulatory bodies and patient groups.
"We will offer all the work that we have done to government when they are ready for us to enter into their consultation process," he said.
"The generous interpretation, I think, of what we have heard from them so far is that they do intend to consult and we are still optimistic that will happen."
Opposition parties said they are not surprised the government has not launched the formal consultation process.
"We haven't seen any action from the government on the issue," said NDP justice critic Francoise Boivin.
"Everybody knows the deadline, February 2016. I smell and sense they kind of prefer to let it be to the future government."
— With files from Stephanie Levitz
Follow @kkirkup and @StephanieLevitz on Twitter
Also on HuffPost