In a statement to The Associated Press, Ensign spokesman Tory Mazzola said the demands from an attorney for Doug Hampton were made within the past month.
"The demands were referred to Senator Ensign's legal counsel, who is handling the matter going forward," the statement said.
Mazzola did not name the attorney nor immediately respond to requests for additional details.
Hampton's lawyer, Daniel Albregts, did not immediately respond to messages seeking comment.
Unconfirmed reports that Doug Hampton was pressuring Ensign for money have circulated since the senator abruptly came forward Tuesday and confessed to a nine-month extramarital affair with Cindy Hampton, his former campaign treasurer and Hampton's wife.
Until Friday, the senator's office had not responded to questions about the allegations.
Ensign, 51, has said he intends to remain in the Senate.
The statement came hours after the Las Vegas Sun published a letter from Doug Hampton to a news organization asking it to expose the senator's "unethical behavior and immoral choice." The nearly 1,000-word letter to Fox News anchorwoman Megyn Kelly accuses Ensign of "heinous conduct and pursuit" of Cindy Hampton, even after both had left their jobs working for Ensign.
A source close to the Hamptons confirmed the letter was written by Doug Hampton. The individual was not authorized to discuss the matter and spoke on condition of anonymity.
Cindy Hampton, 46, was a campaign treasurer for two committees connected to the senator. Doug Hampton served as an administrative assistant on Ensign's Senate staff. Neither have worked for Ensign since May 2008.
The senator acknowledged the affair continued until August 2008.
"Senator Ensign's conduct and relentless pursuit of my wife led to our dismissal in April of 2008," Doug Hampton wrote. "The actions of Senator Ensign have ruined our lives and careers and left my family in shambles."
Ensign's office has said it learned that Doug Hampton had approached a media outlet about the affair when the senator hastily called a news conference to admit his infidelity.
Asked if Fox News received the letter, a company spokeswoman referred the AP to comments from one of its producers that were reported on the Huffington Post, a Web site. Tom Lowell, senior producer of "America's Newsroom," told the Web site that a booker on the show received an e-mail from Hampton with the letter attached on June 15, the day before Ensign's news conference.
Lowell said that when reporters followed up with Hampton, he "seemed evasive and not credible, thus we didn't pursue it."
"Definitely no one on our editorial team called anyone in Senator Ensign's office prior to the announcement," he said.
The letter claims Ensign was confronted by others about his relationship and conduct.
"In fact one of the confrontations took place in February 2008 at his home in Washington DC with a group of his peers," Hampton wrote. "One of the attendee's was Senator Tom Coburn from Oklahoma as well as several other men who are close to the senator."
An aide to Coburn did not immediately respond to a call for comment.
In the letter, Hampton said the Ensigns and Hamptons families were "lifelong friends, our children attend school together to this day, and our homes are in neighborhoods across from each other." He said he went to work for the senator in Washington in November 2006, but since leaving has "lost significant income, suffered indescribable pain and emotional suffering."
After leaving his post, Hampton, 47, quickly landed jobs with companies associated with the senator. He worked briefly for a consulting firm founded by Ensign's closest adviser, Mike Slanker. His biggest client was a Las Vegas-based airline whose executives have contributed generously to Ensign over the years.
Allegiant Air chief executive Maurice Gallagher and his wife have contributed more than $86,000 to Ensign's campaign and political action committees, federal records show.
Hampton later joined Allegiant Air in August 2008 and is currently vice president of government affairs, a company spokeswoman said.
Mazzola said Thursday that the senator made calls recommending Hampton for work after he left the Senate office.
On Friday, Hampton greeted a photographer outside his suburban Las Vegas home and asked for privacy. He handed out a card with his lawyer's name and phone number before driving away.