In the months since the election tech company Smartmatic sued Fox News and three of its anchors, the two companies have engaged in a prehearing back-and-forth that continued Monday when Fox filed briefs in support of a previous motion to have the lawsuit dismissed.

In its defamation suit, which was filed in New York State Supreme Court on Feb. 4, Smartmatic accused Fox and the anchors Lou Dobbs, Maria Bartiromo and Jeanine Pirro of promoting falsehoods about the company and widespread fraud in the 2020 presidential election.

Shortly after the suit was filed, Fox canceled Mr. Dobbs’s program on Fox Business and filed a motion for a dismissal of the suit, arguing that the claims of electoral fraud broadcast on Fox News and Fox Business were newsworthy and handled fairly. Smartmatic replied on April 12, with a brief stating that the three Fox anchors had played along as their guests promoted election-related conspiracy theories.

In its latest volley, Fox asserted that its coverage of Smartmatic was part of its overall reporting on a challenge of the election outcome based on claims made by former President Donald J. Trump.