The parliament says she wrongly used the funds to pay an aide at the National Front's headquarters in Paris.
She says she is the victim of a politically motivated vendetta.
If she does not repay the money, the parliament could now respond by withholding as much as half of her salary and allowances, which her opponents say total almost €11,000 a month.
Ms Le Pen is one of the front-runners in the French presidential election to be held in April and May. If she wins, she has promised a Brexit-style referendum on France's membership of the EU.
Polls suggest that she will make it to the run-off where she is likely to face conservative candidate Francois Fillon or centrist Emmanuel Macron.
"I will not submit to the persecution, a unilateral decision taken by political opponents... without proof and without waiting for a judgement from the court action I have started," she told Reuters news agency on Tuesday.
The money the European Parliament wants returned was used to pay the salary of Catherine Griset, a close friend of Ms Le Pen as well as her cabinet director.
The funds were conditional on Ms Griset spending most of her working time in Brussels or Strasbourg.
However, the parliament says most of her time was instead spent working in the National Front's headquarters in Paris. The party will face a second demand for 41,554 euros in wages paid to her bodyguard.
The far-right leader also tried to distance herself from financial allegations overshadowing Republican candidate Francois Fillon, who has vigorously denied that his wife was paid 834,000 euros for fake jobs.
Asked if she would pay back the money, Marine Le Pen told AFP: "To pay the money back, I'd have had to have received the funds, but my name isn't Francois Fillon."
Quite apart from her refusal to pay back the funds, the FN leader might struggle to find the money. Her party has been unable to raise funds from French banks and has had to seek financing abroad.
In 2014, the FN received a €9m loan from Russian lender First Czech-Russian Bank, which collapsed last year.