Jurors originally found Guy Turcotte not criminally responsible for the 2009 deaths when they accepted his argument he could not remember the events and had experienced blackouts.
Turcotte told the trial he stabbed his children to death and then drank windshield-wiper fluid in what he said was a failed attempt to commit suicide.
The controversial verdict made Turcotte a well-known figure in the province and enraged many Quebecers.
His case was one of several notorious court decisions that helped lead to new federal legislation designed to make it more difficult for those found not criminally responsible to gain their freedom.
The prosecution argued a not-criminally-responsible verdict should be reserved only for cases of mental illness, not ones where a suicide attempt might have triggered an after-the-fact blackout.
The Quebec Court of Appeal sided with such critics when it overturned that verdict last November and ordered a second trial.
A date for the new trial was supposed to be set Friday, but Pierre Poupart, Turcotte's lawyer, announced he wants to go to the Supreme Court in an attempt to challenge the appeals court ruling.
That prompted Quebec Superior Court Justice Marc David to postpone the date-setting until April 4 so he can see what the country's highest court decides between now and then.
David, who presided over the first trial, said any new trial won't take place before March 2015.
Crown spokesman Jean-Pascal Boucher said it could take between three and six months before Canada's top court decides whether it will agree to hear arguments from Poupart.
"Delay in a criminal file is a challenge for both parties, defence lawyers and prosecution, and we will have to deal with it," he said.
He said the Crown will respect the judge's decision to wait for the Supreme Court decision.
"It's the highest court in Canada and we have to respect the criminal process."
Turcotte, meanwhile, will remain behind bars.
He spent 46 months in psychiatric care before being deemed fit for release from a mental institution.
If the second trial finally goes ahead in the spring of 2015, it would take place more than six years after the killings on Feb. 21, 2009.
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