Washington (CNN) -- At a hearing on Thursday that Republicans didn't attend, the nominee for the No. 2 job at the Department of Homeland Security strongly denied reported allegations he helped obtain a special visa for an international investor.
Alejandro Mayorkas told Democrats on a Senate panel considering his nomination by President Barack Obama that he was unaware of being under investigation by a government inspector general until media reports emerged this week.
"I have never, ever in my career exercised undue influence to influence the outcome of a case," Mayorkas said, noting he had yet to be interviewed in the investigation that senators said started last year.
"I look forward to learning about the allegations, as I still don't quite understand them," he added.
An e-mail sent to congressional lawmakers from the homeland security department's inspector general and obtained by CNN said Mayorkas was being investigated, but at this point, "we do not have any findings of criminal misconduct."
Mayorkas currently runs the U.S. Citizenship and Immigration Services, which conducts a foreign investor program known as EB-5 that is the focus of the inspector general's investigation.
According to the e-mail, Mayorkas "was not specifically named in the initial complaint; however, the DHS (office of inspector general) is now investigating allegations concerning the actions/conduct of Director Mayorkas and other USCIS management officials."
The department said its inquiry was launched after a referral from an FBI analyst in the Counterintelligence Unit.
According to the DHS, Mayorkas allegedly helped approve a visa application on behalf of Gulf Coast Funds Management, a company run by Anthony Rodham, the brother of former senator and Secretary of State Hillary Clinton.
The Associated Press -- which first reported the investigation -- said the visa application was made by GCFM on behalf of a Chinese executive. The unnamed applicant was initially found to be ineligible for the EB-5 program, and a subsequent administrative appeal upheld the decision.
Asked about the issue on Thursday, Mayorkas said he took part in discussions with staff about the EB-5 program including complaints by GCFM. Those discussions resolved problems in implementing what he described as the "extraordinarily complex" EB-5 program.
"The allegations as they have been framed are unequivocally false," Mayorkas said, noting that "I did nothing that I haven't done hundreds and hundreds of times when difficult issues reach my attention and the agency needs resolution of them."
He noted that GCFM has complained about his service's handling of EB-5 cases since 2011 and continues do so.
There was no immediate response Thursday to a phone message and email to GCFM seeking comment.
The top Republicans on the Senate Homeland Security and Government Affairs Committee called for putting off consideration of the Mayorkas nomination until after the inspector general's investigation is complete.
A statement by GOP Sen. Tom Coburn of Oklahoma said he boycotted Thursday's hearing because it was unfair to Mayorkas and could hinder the investigation. None of the other Republicans on the panel showed up either.
"Holding this hearing in light of an active investigation into serious, relevant allegations of professional misconduct by the nominee, and over the objections of the ranking member and others, appears to be virtually without precedent in the history of this or any other Senate committee," Coburn said in a statement.
Democratic Sen. Tom Carper of Delaware, the panel's chairman, decided to proceed with the hearing even though only one party took part.
"Rather than allowing rumor and speculation and innuendo to rule the day, this hearing will allow us to continue the process of vetting this nominee," Carper said.
He noted the inspector general's probe began almost a year ago and could last for months or more, which he said was too long for such an important post in the homeland security department to go unfilled.
Carper and other Democrats called Mayorkas an extraordinarily qualified nominee, citing his record as a U.S. prosecutor in California and as head of the customs and immigration service.
The EB-5 program grants expedited visa approval for foreigners who invest up to a $1 million in a business that creates American jobs. The visa approval also allows eligible foreigners to gain naturalized status and eventual citizenship.
According to the internal DHS e-mail, the inspector general is investigating whether other U.S. government officials obstructed an audit of the EB-5 visa program by the Securities and Exchange Commission.
Recent media reports indicated GCFM had helped finance a green energy company formerly run by Terry McAuliffe, who is running for governor of Virginia as a Democrat.
McAuliffe is a former top political adviser and fundraiser for President Bill Clinton and Hillary Clinton. He also ran the Democratic National Committee from 2001 to 2005.
McAuliffe reportedly cut ties with the energy firm GreenTech late last year.
On Thursday, Mayorkas recalled a meeting with McAuliffe to listen to complaints about the handling of an EB-5 case.
"I heard those complaints and that was the extent of that interaction," Mayorkas said.
Asked by Carper if he made any changes based on the meeting with McAuliffe, Mayorkas answered "absolutely not" and added: "I do remember returning to the office and complaining about the fact that I had to hear complaints. That is all."
McAuliffe's Republican opponent said the allegations were serious.
"I think it's time for Terry McAuliffe to come forward and answer questions about this serious matter," Virginia Attorney General Ken Cuccinelli said in a statement. "Virginians deserve to know the truth about McAuliffe and GreenTech's potentially inappropriate solicitation of EB-5 visas."
McLean, Virginia-based GCFM specializes in securing visas for foreign investors. Its website offers a pitch to such investors: "We will use our knowledge of the region to make investments in projects that will create enough jobs for you to receive your permanent residency status and provide strong opportunities for capital preservation and potential capital appreciation."
CNN's Virginia Nicolaidis, Bill Mears and Ted Barrett contributed to this report.