Democratic gubernatorial candidate Terry McAuliffe campaigns at a George Mason University campus in Arlington, Va., on May 9. (Linda Davidson/THE WASHINGTON POST)

President Obama’s pick for the No. 2 job at the Department of Homeland Security acknowledged Thursday that he had met with prominent Democrat Terry McAuliffe, who wanted to complain about the agency’s slow visa application process.

But Alejandro Mayorkas said he did nothing improper to help McAuliffe, describing accusations to that effect as “unequivocally false.”

Mayorkas, director of U.S. Citizenship and Immigration Services (USCIS), is under scrutiny by the department’s inspector general over allegations that he mismanaged a visa program for foreign investors used by McAuliffe’s car firm, GreenTech, according to congressional aides and documents.

“I was asked to attend a meeting with Mr. McAuliffe so that I could hear in person his complaints. . . . I heard those complaints, and that was the extent of the interaction,” Mayorkas said.

McAuliffe, the former Democratic National Committee chairman, is the party’s nominee in the high-profile race for Virginia governor, and the visa issue has seeped into the contest. The campaign of McAuliffe’s GOP opponent, Attorney General Ken Cuccinelli II, has sought to portray McAuliffe as not “capable of telling the truth.”

The IG investigation has also complicated Mayorkas’s path to confirmation as deputy secretary of Homeland Security. Republicans, who want the nomination delayed, boycotted Thursday’s hearing before the Senate Homeland Security and Governmental Affairs Committee.

“I have never in my career used undue influence to influence the outcome of a case,” Mayorkas told the committee. Mayorkas testified that he met with McAuliffe roughly two years ago about the visa program. He said such meetings were common and he considered them part of his job.

He added that being “accused of tipping the scales” in favor of Gulf Coast Funds Management — the Anthony Rodham firm that processes GreenTech’s visas — after “referring the matter to the Fraud Detection and National Security Directorate for appropriate action based upon a question of . . . the project’s integrity seems a bit contradictory.”

The fraud directorate, set up by Mayorkas, reviews “background check information and other concerns that surface” in the course of considering immigration applications.

Earlier this week, McAuliffe spokesman Josh Schwerin said the inspector general’s probe “does not involve Terry.” On Thursday, Schwerin described the meeting as a routine effort by McAuliffe to help his business.

“Terry, like many business and political officials from both parties, was frustrated with the bureaucratic pace of the investment program,” Schwerin said. “As was made clear today, there has been widespread frustration inside and outside USCIS about the bureaucracy there, and Terry was among those who expressed frustration with that bureaucracy.” Schwerin said McAuliffe was unaware that Mayorkas was the subject of any investigation until news reports this week.

Republicans, led by Sen. Tom Coburn (Okla.), had called on Democrats to delay Thursday’s hearing. Coburn said it was likely unprecedented for a committee to hold a hearing over the objections of the minority and “in light of an active investigation into serious, relevant allegations of professional misconduct by the nominee.”

But Chairman Thomas R. Carper (D-Del.) refused, saying in a statement that he would not allow “rumor, speculation, and innuendo to rule the day.” Carper said Mayorkas had never been notified that he was the subject of a probe.

“The Office of Inspector General apparently does not have any ‘preliminary findings’ regarding Mr. Mayorkas,” Carper said in prepared remarks before the hearing. “In fact . . . the Office of Inspector General has found no wrongdoing by Mr. Mayorkas.”

If confirmed as second-in-command at DHS, Mayorkas would temporarily lead the department after the scheduled departure of Secretary Janet Napolitano in early September.

The inspector general’s probe centers on the EB-5 visa program, which permits foreign nationals to enter the United States if they agree to invest $500,000 to $1 million to create U.S. jobs. The IG launched the inquiry last year on a tip from an FBI counterintelligence analyst concerned about the program, which is dominated by applicants from China, according to congressional aides.

E-mails show that Mayorkas’s assistance was sought in January by Rodham, who runs Gulf Coast Funds Management of McLean, which pools money from foreign citizens who want to invest in U.S. businesses as part of the EB-5 program.

Rodham and other Gulf Coast officials wrote to Mayorkas and other DHS officials asking for help with delays that they said were harming GreenTech Automotive, which was co-founded by McAuliffe. McAuliffe quietly resigned as chairman of the company sometime before Dec. 1.

Critics have previously raised questions about GreenTech’s use of the visa program. When the company was considering putting a factory in Virginia, a state economic-development official wrote to a colleague that she worried the venture was “a visa-for-sale scheme with potential national security implications.”

In his testimony Thursday, Mayorkas called the EB-5 program “controversial and extraordinarily complex,” noting that he receives more complaints about it than any other program he administers.

But Mayorkas said no one got special treatment. “We do what the laws and the facts require and nothing more,” he said.