The so called 'in-and-out' dispute began when an Elections Canada auditor looked into the party expenses and said the Conservatives violated campaign financing rules.
Elections Canada maintains the party funnelled money for national ads through 67 local candidates, allowing the party to exceed its spending limit and allowing candidates to claim rebates on expenses they hadn't actually incurred.
Last November, the Conservative party pleaded guilty to election financing charges and paid the maximum fine of $52,000.
Charges against four senior party officials were dropped as part of the plea deal, which also prevented evidence being made public in court.
The party tried to force Elections Canada to pay rebates to candidates who claimed the disputed advertising as part of their local campaign expenses.
It won the first round in that battle but lost on appeal. The party later won leave to appeal the matter to the Supreme Court of Canada and a tentative date for a hearing had been set for May 14.
Fred DeLorey, Conservative party spokesman, said in a statement to the media Tuesday that "we are agreeing to disagree and will be dropping our appeal to the Supreme Court."Suggest a correction