A counter-claim by Tiffany for 541.9 million francs ($589 million) "has no factual or legal basis and will be vigorously contested by Swatch Group and Tiffany Watch Co. Ltd.," a statement said.
Tiffany Watch is an affiliate of Swatch that was established in 2008 in cooperation with the US firm.
In September however, Swatch broke off a cooperation agreement with Tiffany & Co. for "breaches of its obligations and duties," and sought compensation of 3.8 billion francs in damages.
Swatch said it had invested "millions to develop, distribute and sell Tiffany & Co. watches" but that the venture was undermined by "systematic efforts to block and delay development of the business" by Tiffany & Co.
Tiffany has alleged that Swatch broke its promises and failed to provide appropriate distribution for Tiffany-branded watches, depriving it of the increase in watch sales and royalty income it had been seeking.
Shares in Swatch slipped by 0.35 percent to 423.50 Swiss francs in early trading on Monday, while the Zurich stock exchange was off by 0.16 percent overall.
Analysts at the Zurich cantonal bank ZKB said it was difficult to judge which company would prevail.