PARIS, France — L'Oreal said on Thursday it would appeal a €2.6 million ($3.05 million) fine imposed by Greece's competition authority, which ruled that the French cosmetics company and several of its rivals were fixing prices.

The local beauty products business of France's Christian Dior — part of luxury goods group LVMH — was also fined just under €1.8 million ($2.1 million), while US-based Estée Lauder got the biggest fine, at €5.4 million ($6.3 million).

Greece's anti-trust commission fined six cosmetics companies a total of €18.7 million ($21.9 million) after investigating allegations that luxury cosmetics wholesalers were agreeing on the discounts to be applied to their products when resold in shops and indirectly fixing prices as a result. Three Greek companies were included in the six.

"L'Oreal Hellas denies any accusations of unlawful competition," the company said. L'Oreal, which owns brands such as Lancome and Kiehl's, is the world's biggest cosmetics and beauty products company.

Christian Dior could not immediately be reached for comment. Estée Lauder said in a statement it was "reviewing the authority's decision with the intention to appeal."

Greece's Sarantis, which was slapped with a €1.9 million ($2.2 million) fine, had also said on Wednesday that it would appeal the ruling and disputed the size of the fine.

"There had never been any kind of agreement between the distributors of luxury cosmetics in Greece with the aim to set cosmetics sale prices," Sarantis said in a statement. Sarantis also has a 49 percent stake in a joint venture with Estée Lauder in Greece.

By Pascale Denis and Sarah White; Editor: Jane Merriman