Republican presidential candidate Donald Trump speaks at a campaign stop in Portland, Maine, on Thursday, March 3, 2016. (AP Photo/Robert F. Bukaty)

Donald Trump has claimed  he has the "world's greatest memory," but when it came time this winter to give testimony in fraud cases filed against him and a real estate training program known as "Trump University," he displayed a repeated inability to recall names and faces of instructors he had claimed to have hired personally.

"I can't remember that," he said on Dec. 10, when asked by trial lawyers in one of the class-action cases whether he had met one of the instructors in a program that provided training in building wealth through real estate.

"The name sounds familiar but its too many years," he said when asked about the next name. "Too many years," he answered more than a dozen times.

Trump's comments were contained in two previously confidential depositions released  late Thursday in a court filing in federal district court in San Diego. His previously undisclosed testimony was obtained on Dec. 10 and again  on Jan. 21 in connection with lawsuits against him and Trump University.  Trump has consistently rejected the fraud allegations and pointed out that the institution bearing his name received high ratings from nearly all who participated.

"Mr. Trump’s deposition was simply Plaintiffs’ chance to elicit information in hopes of making a case," Jill A. Martin, vice president and assistant general counsel to the Trump organization, said in a written statement Thursday evening. "It does not contain Mr. Trump’s side of the case, which will be presented in court proceedings and which will demonstrate that plaintiffs' lawsuit has no substance." She added that "Trump University was a professionally run company which provided students with a valuable and substantive education and the tools to succeed in business and real estate.  Those students that applied these strategies were overwhelmingly satisfied and many were able to make substantial profits."

That was not the view of New York Attorney General Eric Schneiderman who filed a $40 million fraud suit against Trump and Trump University in 2013 alleging that Trump had defrauded more than 5,000 individuals through the unlicensed institution. Two other class-action lawsuits have been filed by students asking for their money back and the depositions were obtained in connection with those suits. Schneiderman alleged in the suit that Trump personally earned $5 million from the enterprise, in which sales personnel were assigned the goal of getting people to pay $1,495 for a three-day seminar in real estate techniques.

Marco Rubio accused Donald Trump of starting a "fake university" at the Feb. 25 GOP debate in Houston. Here's what you need to know about Trump University. (Peter Stevenson/The Washington Post)

To attract students, Trump released a marketing video that pledged "we are going to have professors and adjunct professors that are absolutely terrific. . . and these are all people who are going to be handpicked by me." One of the university's top executives, Michael Sexton, subsequently testified in one of the class-action suits that "none of the professors at the live events" were handpicked by Trump. The depositions released Thursday quote Trump acknowledging a lack of close involvement with mentors and students.

"Did you do anything personally to confirm the expertise of any of the Trump University mentors?" Trump was asked in the depositions released Thursday. "No, I didn't," he responded.

Trump has repeatedly denied any wrongdoing in the university's marketing and collection of fees. Still, his conduct has become an issue in the presidential campaign in part because a super PAC has launched ads critical of the operation of the school that bears his name. The super PAC, American Future Fund, aired the ads after fraud allegations against Trump University were raised by Florida Sen. Marco Rubio during the Feb. 25 Republican presidential debate.

As he has said publicly, Trump insisted under oath that many Trump University attendees were satisfied with their experience. Told by a lawyer for the plaintiffs that 25 percent of university attendees had requested refunds, Trump compared the university to the Home Shopping Network, which has loose refund rules and therefore also has a high refund rate.

"You go to the Home Shopping Network, whatever it's called. The refunds are unbelievable. The people use the product, wear the product, and then they send it back," Trump said. " So you know, when people were asking for their money back, frankly -- and I would have these good reports, but people would ask for their money back -- we gave them their money back. I shouldn't have given their money back. I gave back millions of dollars because I'm an honest guy."

Being required to sit for a sworn deposition in the middle of a presidential political campaign presents obvious political peril. For instance, a lawyer in the Trump University suit asked a series of questions about Trump's past praise for former president Bill Clinton, former secretary of state Hillary Clinton and various of his Republican rivals at the time. Trump was then required to answer those questions under oath.

"Yeah, at the time I might have," Trump responded when asked if he believed Hillary Clinton would make a "great president or vice president," as he had written in a March 2008 blog item. "I didn't give it a lot of thought, because I was in business. And, as a businessman, I think it was something I never really gave much thought to. Now that I see what she's done and how she's handled herself and how she's handled her e-mails and all of the problems that she's got, I would say she wouldn't make a very good vice president or president."

The depositions were released Thursday as exhibits attached to a filing in the latest legal wrangling in the long-running dispute. The new documents show that Trump spent considerable time personally engaged in the litigation, even in the heat of the campaign. He sat for one deposition in New York on Dec. 10 from 10:05 a.m. until 5:02 p.m. He then sat again for nearly three hours in Las Vegas, concluding the deposition just three hours before he appeared in front of a rally in the city.

"This is the longest deposition I've ever done in terms of no break," Trump complains at one point during the questioning. "So I need breaks because I have to make some calls."