By Jonathan Stempel

(Reuters) - Lawyers for Fox News chairman Roger Ailes on Friday asked a judge to halt anchor Gretchen Carlson's "shameless publicity campaign" against her former boss, and send her sexual harassment lawsuit against him to arbitration in accordance with her employment contract.

The request came two days after Carlson sued Ailes in Superior Court in New Jersey, portraying him as a persistent harasser who demoted her and ultimately forced her from Fox News, her employer since 2005, after she rebuffed his advances. Ailes has forcefully denied Carlson's allegations.

Carlson's lawyers, Nancy Erika Smith and Martin Hyman, said their client intends to pursue her right to a public jury trial.

"Roger Ailes is trying to force this case into a secret arbitration proceeding," the lawyers said in a statement. "Gretchen never agreed to arbitrate anything with Mr. Ailes."

The parent of Fox News, 21st Century Fox Inc, late on Wednesday said it had "full confidence" in Ailes and began an internal review of the matter.

In filings with the federal court in Newark, New Jersey, Ailes' lawyers said Carlson's June 2013 contract required her to arbitrate any employment disputes.

They accused Carlson of "gamesmanship" for suing only Ailes and not the network as well, calling it a legally improper means to avoid arbitration, and of conducting a public "tar and feather" campaign to sully Ailes' reputation.

The lawyers also said that under federal law the case did not belong in the New Jersey state court because Carlson lived in Connecticut and Ailes in New York, and the amount of money at stake was too high.

"Plaintiff's ploy of filing in Superior Court to justify her shameless publicity campaign against Roger Ailes should not be countenanced," the lawyers said.

Friday's filings included a copy of what Ailes' lawyers said was Carlson's employment contract, which calls for employment disputes to be heard by a three-person arbitration panel.

Ailes, 76, a former Republican political consultant and confidant of 21st Century Fox Executive Co-Chairman Rupert Murdoch, has built Fox News over two decades into the most-watched U.S. cable news channel and become one of the most powerful American media executives.

In her lawsuit, Carlson, 50, accused Ailes of sexually inappropriate conduct such as calling her a "man hater," ogling her in his office and telling her she was "sexy" but "too much hard work."

Carlson said Ailes removed her in 2013 as co-host of the morning show "Fox & Friends" in retaliation for her refusal to accept his advances and reassigned her at lower pay to an afternoon show. She also said his decision on June 23 not to renew her contract was retaliatory.

The federal case is Carlson v Ailes, U.S. District Court, District of New Jersey, No. 16-04138.

(Reporting by Jonathan Stempel in New York; Editing by Chris Reese and Cynthia Osterman)