Dr. Melgen's attorney issued the following statement Thursday:
"The government has not informed Dr. Melgen what concerns it may have. We are confident that Dr. Melgen has acted appropriately at all times. Additionally, any issues concerning Dr. Melgen and the IRS have been fully resolved and satisfied."
The statement from Menendez's office described Melgen as a friend and political supporter and said the senator had traveled on Melgen's plane three times.
In April the watchdog group Citizens for Responsibility and Ethics in Washington, known as CREW, started receiving e-mails from someone alleging Menendez had made several trips to the Dominican Republic and partied with prostitutes. CREW was unable to verify the claims and forwarded the information to the FBI and the criminal division at the Justice Department.
Shortly before the November election, a conservative website, The Daily Caller, ran stories saying Menendez had flown to the Dominican Republic on Melgen's plane and engaged with prostitutes. Prostitution is legal in the Caribbean nation.
"Any allegations of engaging with prostitutes are manufactured by a politically motivated right-wing blog and are false," Menendez's office said in its Wednesday statement.
Meanwhile, New Jersey state Sen. Sam Thompson, a Republican, sent a complaint to the Senate Ethics Committee in November calling for an investigation, saying Menendez may have violated Senate ethics by "repeatedly flying on a private jet to the Dominican Republic and other locations ... and soliciting prostitutes." Thompson said he did not hear back from the Ethics Committee.
Menendez made the payment following an exhaustive review of his travel conducted by his chief of staff Danny O'Brien in the wake of Thompson's complaint.
Enright said it was an "oversight" on the part of the senator not to have paid for the flights at the time he took them. She could not explain why the veteran lawmaker didn't know to fully disclose the flights at the time.
Enright said the New Jersey GOP ethics complaint alleged four flights but Menendez's initial review found that he was not on two of the flights mentioned in the complaint and a third flight was for official DSCC business. Since they couldn't account for the one flight, his office decided to conduct the review which turned up one other flight.
Menendez's campaign counsel advised that because the senator and doctor are old friends, he could have claimed a friendship exemption. But Menendez decided he would prefer to pay for everything and wrote the $58,500 check from his personal funds.
Both the Senate Ethics Committee and the FBI said they could not comment and that their policies are to never confirm whether they are conducting investigations.
Menendez, who is divorced, is in line to become the chairman of the Senate Foreign Relations Committee. The senator has not been contacted by the ethics committee but assumes it is reviewing the matter. He has no plans to resign over the issue, Enright said.
Federal Election Commission records show Melgen has made at least $193,000 in election contributions since 1998, including more than $14,000 to Menendez's Senate campaigns. Records show the doctor also donated $5,000 to Menendez's political action committee.
U.S. Senator Bill Nelson is one of a handful of democratic politicians Melgen has made campaign contributions
to over the last decade. Nelson's press office says Melgen made two contributions, one in 2000, and another in 2006.
"We don't know this guy from Adam," says Dan McLaughlin, Director of Communications for Senator Bill Nelson. "He is one of a million people who have made a contribution to Nelson's campaigns over the years."
CNN contributed to this report.