E. Jean Carroll, right, talks to reporters outside Manhattan Supreme Court, Wednesday, March 4. Her attorney Roberta Kaplan is at left. Photo: Seth Wenig/AP

Roberta Kaplan, the attorney for an author and advice columnist who has sued President Donald Trump for defamation, said in a Manhattan Supreme Court appearance Wednesday that some forms of discovery should advance while New York's highest court weighs whether a president can be haled into state court over nonofficial conduct.

But lawyers for Trump said that since he is claiming immunity from lawsuit during his term of office, he is asserting a constitutional right and all discovery should halt while the New York Court of Appeals.

Both sides agreed that a deposition of Trump and a DNA test should not take place until the New York Court of Appeals issued a decision in a case captioned Zervos v. Trump that tests the immunity claim.

But that was about the only note of accord in the appearance before New York County Supreme Court Justice Verna Saunders.

The hearing was the latest in a case brought by the author, E. Jean Carroll, who is suing Trump over his denial of her allegation that he raped her in a Manhattan department store in the 1990s. Trump, in denying the allegation, said among other things that he had never met her and that she made up her story.

Marc Kasowitz of Kasowitz Benson Torres, who is representing Trump, has argued that the case must be stayed until the New York Court of Appeals issues its decision in Zervos, another defamation case against Trump.

In Carroll's case as well as Zervos, Trump has asserted that the Supremacy Clause of the U.S. Constitution precludes a sitting president from being brought into state court for conduct that is not related to his federal duties.

During oral arguments Wednesday, Kasowitz partner Christine Montenegro noted that a federal case that could provide some guidance—Trump v. Vance, which deals with whether a state grand jury can subpoena materials relating to the president—is set to be heard before the U.S. Supreme Court in just a few weeks.

Kaplan of Kaplan Hecker & Fink, told Saunders that the plaintiff's team is willing to delay Trump's deposition and its request for his DNA test until the Court of Appeals has reached its decision in Zervos.

Carroll is seeking the DNA test because there is "unidentified male DNA on the dress that Carroll wore during the attack," according to court papers.

Kaplan said delaying Trump's deposition while proceeding with other discovery involving Carroll, the store where the alleged attack took place and other parts of her account is "a very practical way of organizing" the process.

But lawyers for Trump said an incremental approach could still cause a violation of his constitutional rights.

"That's not sufficient, because we're asking for immunity from a lawsuit," Montenegro said in court. "It's a constitutional right."

Kaplan accused Trump of "cherry-picking" cases, asserting immunity from some lawsuits and moving forward with others. She said the volume of Trump's personal litigation is unlike that of any previous president.

Montenegro disagreed with the allegation of cherry-picking, saying that some of Kaplan's examples are federal cases bound by different rules and another, a brand-new case in which the Trump campaign sued The New York Times, does not involve the president himself.

The Zervos case—which bears a resemblance to Carroll's in that it is a defamation claim over Trump's denial of a sexual misconduct allegations—is not likely to be argued until the fall, Kaplan said.

In Zervos, the plaintiff, Summer Zervos, a former contestant on "The Apprentice" reality competition program, sued Trump for allegedly calling her a liar.

Read more:

Defamation Lawsuit Against Donald Trump Can Be Heard by NY Court of Appeals, First Department Rules

Roberta Kaplan Files Lawsuit Alleging Trump Defamed Author as Liar in Wake of Rape Accusation

'They're Making This Up': Manhattan Prosecutor Hits Back at Trump Lawyers' Claim of Immunity From State Criminal Procedures