A New York judge said Wednesday he’s close to releasing President Trump from a contempt finding if he meets certain conditions, including paying $110,000 in fines accrued for failing to turn over documents in a state civil investigation.

Judge Arthur Engoron said he will conditionally lift Mr. Trump’s contempt finding if, by May 20, Mr. Trump submits additional affidavits detailing efforts to search for records and explaining his and his company’s document retention policies, a company he hired to aid the search completes its work, and he pays the fines.

Judge Engoron ruled Mr. Trump in contempt on April 25 and fined him $10,000 per day for not complying with a subpoena for documents in the New York attorney general’s investigation, which is probing whether Mr. Trump may have misstated the value of assets like skyscrapers and golf courses on financial statements for over a decade.

The total Judge Engoron ordered Mr. Trump to pay is the fine accrued through May 6, when Mr. Trump’s lawyers submitted 66 pages of court documents detailing efforts to locate the subpoenaed records. Judge Engoron could reinstate the fine if the conditions he set forth on Wednesday are not met.

A message seeking comment was left with Mr. Trump’s lawyer.

Ms. James, a Democrat, asked Judge Engoron to hold Mr. Trump in contempt after he failed to produce any documents to satisfy a March 31 deadline to meet the terms of the subpoena.

Trump attorney Alina Habba said in the May 6 filing that the responses to the subpoena were complete and correct and that no relevant documents or information were withheld.

Ms. Habba conducted searches of Mr. Trump’s offices and private quarters at his golf club in Bedminster, New Jersey, and his residence in Mar-a-Lago, Florida, according to the filing, but didn’t find any relevant documents that hadn’t already been produced. The filing also detailed searches of other locations including file cabinets and storage areas at the Trump Organization’s offices in New York.

In a separate sworn affidavit included with the filing, Mr. Trump stated there aren’t any relevant documents that haven’t already been produced.

He added that he owns two cellphones: an iPhone for personal use that he submitted in March to be searched as part of the subpoena, then submitted again in May; plus a second phone he was recently given that’s only used to post on Truth Social, the social media network he started after his ban from Twitter, Facebook, and other platforms.

Also Wednesday, a state appellate court is scheduled to hear oral arguments in Mr. Trump’s appeal in another subpoena matter: Judge Engoron’s February 17 ruling requiring him to answer questions under oath in Attorney General Letitia James’s investigation.