Guy Turcotte was hoping the high court would hear his case for overturning a lower court decision in an attempt to avoid a second first-degree murder trial in the killings.
As is standard practice in the case of applications for leave to appeal, the Supreme Court did not give reasons for its decision to reject Turcotte's bid.
Turcotte will face trial again for the deaths of his children, Olivier, 5, and Anne-Sophie, 3, who were stabbed a combined 46 times before Turcotte tried to take his own life by ingesting windshield washer fluid.
His highly publicized trial heard that Turcotte was distraught over the abrupt end of his marriage and only remembered the night in flashes.
A spokesman for the Crown's office said it was satisfied with the Supreme Court's decision and is ready to proceed with a trial.
"The prosecutor in charge of the file will continue his preparation in view of the new trial," said spokesman Jean-Pascal Boucher.
Boucher said a date for the trial will likely be set on April 4, when the case is scheduled to return to court in St-Jerome.
Turcotte was originally found not criminally responsible in the 2009 stabbing deaths, a decision that enraged many Quebecers.
He was briefly confined to a mental health facility following the verdict, but convinced an independent board that he should be freed.
All told, he was confined for about 46 months.
Last November, the Quebec Court of Appeal overturned the 2011 jury verdict and ordered the new trial on two counts of first-degree murder.
The province's top court said the judge made certain legal errors that opened the door to a new trial.
The mother of the two young victims said she took in the high court decision with mixed emotions.
"I was happy for about 10 minutes until I realized in my head all the effort and agony that I will, myself, and the other witnesses, will have to go through again," Gaston told The Canadian Press.
Gaston was a fixture at the first trial but wasn't sure she'd be there every single day this time around. Although satisfied with Thursday's decision, she acknowledged she had some anxiety about the upcoming trial.
"Olivier, Anne-Sophie, I want there to be justice for them, if we can speak of justice," Gaston said, adding in the end, there may be none at all.
Turcotte was re-arrested after the appeal court decision and is currently detained.
The judge hearing the case put off setting a new trial date until the Supreme Court made its decision. He also said the earliest a new trial could take place is sometime in 2015.
— With files from Canadian Press reporter Magdalene Boutros in Montreal.
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