“We are confident that the good men and women of the Bronx will hold Fox accountable for what we believe to be its abhorrent racist conduct, reminiscent of the Jim Crow era,” the plaintiffs’ lawyers, Douglas H. Wigdor and Jeanne Christensen of the Wigdor law firm, said in a statement. The firm also represents two employees of The New York Times in a pending federal lawsuit against The Times, alleging age, race and gender discrimination.

Ms. Brown and Ms. Wright are suing Ms. Slater, Fox News and its parent company, 21st Century Fox, claiming that Ms. Slater’s superiors did little to address her behavior, which created a hostile work environment that resulted in “severe and pervasive discrimination and harassment.”

Ms. Wright, who joined Fox in mid-2014 and had spoken up about Ms. Slater’s behavior, was transferred out of the payroll department on Monday, a move the lawsuit described as a demotion. The company described it as a lateral move. While the suit contends that Ms. Brown, who joined Fox in late 2008, was fired on Monday, the company said on Tuesday night that she remained employed. Both women declined a Fox settlement offer, according to the suit.

The company said on Tuesday night that it took immediate action after learning about the allegations against Ms. Slater and fired her on Feb. 28.