NEW YORK -- A judge set deadlines possibly making President Donald Trump answer questions under oath by early next year in a former "Apprentice" contestant's defamation suit, while Trump's lawyers pushed back Tuesday on demands for information on his campaign's discussions about other women who also accused him of sexual misconduct.

Trump's legal team continues to try to get Summer Zervos' defamation lawsuit dismissed or delayed until after his presidency. But at least for now, it's moving into an information-gathering phase potentially involving key disclosures -- and put both Trump and Zervos under questioning by each other's lawyers.

Zervos accuses Trump of slurring her by calling her a liar. Already, her lawyers have issued subpoenas seeking a range of information, including any records concerning his 2016 campaign's responses to Zervos' and other women's accusations of inappropriate sexual behavior. Trump has vehemently denied them all as made-up.

At a court hearing Tuesday, Trump lawyer Marc Kasowitz said the campaign shouldn't have to turn over any material about other women.

It's "irrelevant," he said.

Not so, said Zervos' attorney, Mariann Wang.

"It's a defamation case, so we are required to prove the falsity of the statements, and his statements include statements about other women," she said outside court.

Manhattan state Supreme Court Justice Jennifer Schecter didn't settle the dispute Tuesday but began setting various deadlines, including Jan. 31 for any depositions of Trump and Zervos. Lawyers for each have indicated they want to depose the other's client.

If they do, each side will have up to seven hours.

Presidential depositions have a memorable history: During a 1998 deposition in a sexual harassment case filed by Paula Jones, then-President Bill Clinton denied a sexual relationship with White House intern Monica Lewinsky. Clinton's denial eventually led to his impeachment by the House of Representatives for perjury and obstruction of justice; the Senate ultimately acquitted him.

Despite the deadline, it's too soon to say for sure when Trump might have to submit to questioning. His lawyers plan to argue to a state appeals court this fall a sitting president can't be sued in a state court, and Kasowitz indicated Tuesday the question could end up at the U.S. Supreme Court.

He also said Trump might seek extensions on various case deadlines because of the "significant attendant duties" of the presidency.

Zervos, a California restaurateur, appeared in 2006 on Trump's former reality show, "The Apprentice." She says he subjected her to unwanted kissing and groping when she sought career advice in 2007.

She was among more than a dozen women who came forward late in the 2016 presidential campaign to say Trump had sexually harassed or assaulted them.

The Republican denied all the claims, saying they were "100 percent fabricated" and "totally false" and his accusers were "liars." He specifically contested Zervos' allegations in a statement and retweeted a message including her photo and described her claims as a "hoax."

Zervos says his words hurt her reputation, harmed her business and led to threats against her. She is seeking a retraction, an apology and compensatory and punitive damages.