“Thus far in our investigation, we have uncovered significant evidence that suggests Donald J. Trump and the Trump Organization falsely and fraudulently valued multiple assets and misrepresented those values to financial institutions for economic benefit,” Ms. James, a Democrat, said.

The Trumps have asked a judge to quash the subpoenas or put them on hold until a parallel criminal case has concluded. Lawyers for the Trumps have argued that any information the attorney general’s lawyers gained through depositions could be improperly used in the criminal investigation, which the Manhattan district attorney’s office is conducting alongside lawyers from the attorney general’s office.

Alan Futerfas, a lawyer for Donald Jr. and Ivanka Trump, said that in the filings the attorney general’s office hadn’t addressed the Trumps’ core arguments.

“In 160 pages of legal briefing, the Attorney General’s Office deliberately fails to address Ms. James’s repeated threats to target the Trump family and her assertions about her criminal investigation—all which are the essence of our motion to quash the subpoenas or stay them,” Mr. Futerfas said.

A spokeswoman for the Trump Organization said Ms. James’s allegations were baseless. “She defrauded New Yorkers by basing her entire candidacy on a promise to get Trump at all costs without having seen a shred of evidence and in violation of every conceivable ethical rule,” the spokeswoman said. Ms. James has previously defended her investigation, saying no one is above the law.

A lawyer for Donald Trump didn’t respond to a request for comment.

The office has said its investigation began in March 2019, after former Trump lawyer

Michael Cohen

testified before Congress that Mr. Trump deflated his assets to decrease real-estate taxes and inflated them to gain financial benefits.

Ms. James’s office said it determined that Mr. Trump made inaccurate statements in his statements of financial condition, a collection of financial information compiled but not audited by his accountants that contained values for properties and assets.

The inaccuracies pertained to Trump properties including Seven Springs, an estate north of New York City; Mr. Trump’s triplex apartment in Trump Tower; and the Trump International Golf Club Scotland, the attorney general’s office said.

To value Mr. Trump’s apartment, the statements based a calculation on the assertion that the triplex was 30,000 square feet, despite the actual size being 10,996 square feet, the attorney general’s office said. The 2015 and 2016 statements valued the apartment at $327 million, based on the 30,000-square -foot size, according to the office.

The attorney general’s office said its evidence showed banks and financial institutions relied on the statements when determining whether to grant Mr. Trump and his company loans and insurance.

Write to Corinne Ramey at Corinne.Ramey@wsj.com