The LFP oversees all matters concerning the top two tiers of football in France, but PSG said they would seek a legal ruling elsewhere.
The forward says PSG owe him 55 million euros in wages and bonuses, but the Parisians say Mbappe agreed to waive the money in August 2023.
On Thursday, the LFP commission told PSG to pay, reportedly within a week, sparking a response from the Qatari-backed club.
"Given the limits of the Commission's legal scope to make a full decision on this matter, the case must now be pursued before another court," the club said.
"PSG will look forward to presenting all the facts over the coming months and year."
Lawyers representing the two parties met early on Wednesday after Mbappe, who joined Real Madrid this summer, had referred his case to the LFP's legal committee.
