Updated

President Obama's nominee for the No. 2 spot at the Homeland Security Department on Thursday "unequivocally" denied allegations that he improperly helped a company run by Hillary Clinton's brother obtain a visa, as Republicans boycotted his confirmation hearing over the matter.

Alejandro Mayorkas, the director of U.S. Citizenship and Immigration Services, is under investigation by the department's inspector general. Despite calls by Republicans to postpone it, he testified at his confirmation hearing Thursday morning before the Senate Homeland Security and Governmental Affairs Committee.

He said he "made no orders" in these cases, and that he only offers guidance based on the "facts" and "the law."

"I have never, ever in my career exercised undue influence to influence the outcome of a case," he said. He said he had "no idea" he was under investigation and "quite frankly, I still don't understand it."

Mayorkas encountered a largely friendly audience, as he dealt with questions from Senate Democrats. Republicans boycotted the hearing, after having tried unsuccessfully to get the hearing postponed.

"I cannot participate in a hearing I believe to be unfair and improper to all parties involved," Sen. Tom Coburn, R-Okla., said in a statement.

Republicans, in a letter Wednesday to committee Chairman Sen. Tom Carper, D-Del., claimed the news of the investigation took them by surprise. They said neither the White House nor Mayorkas had disclosed the existence of the probe to them before -- the investigation was first reported on Tuesday.

"We believe it is neither appropriate nor fair to consider the nomination of an individual under investigation," the lawmakers wrote. The letter was signed by Sens. John McCain, R-Ariz.; Rob Portman, R-Ohio; Ron Johnson, R-Wis.; and Coburn. They said lawmakers would be hamstrung in asking about an ongoing investigation during the hearing, yet would need to know those details in order to fairly consider the nomination.

Sen. Charles Grassley, R-Iowa, also wrote committee leaders asking for a postponement "until the facts are more fully developed."

The White House is doubling down on the pick, who if confirmed could temporarily lead the department. In a brief letter to Carper on Wednesday, White House Counsel Kathryn Ruemmler assured that the nominee underwent a "thorough" FBI background check before the nomination and "we have no concerns about his suitability for this important position."

The Inspector General's Office, though, has not closed the book on the case.

The office has confirmed that it is investigating Mayorkas' role in helping secure a foreign investor visa for Tony Rodham's Gulf Coast Funds Management even after the application was denied and an appeal rejected.

In a statement, the office said he was not initially a target of the investigation. But as the probe progressed, "subsequent allegations have been identified involving alleged conflicts of interest, misuse of position, mismanagement of the EB-5 program, and an appearance of impropriety by Mayorkas and other USCIS management officials."

The international investor visa program run by USCIS, known as EB-5, allows foreigners to get visas if they invest $500,000 to $1 million in projects or businesses that create jobs for U.S. citizens. The amount of the investment required depends on the type of project. Investors who are approved for the program can become legal permanent residents after two years and can later be eligible to become citizens.

In an email to lawmakers Monday, the IG's office said "at this point in our investigation, we do not have any findings of criminal misconduct."

Congressional officials briefed on the investigation said the visa was for a Chinese executive. Homeland Security and Citizenship and Immigration Services have not commented on the investigation.

Rodham's company said Tuesday it was not aware of the investigation or of any investor visa application being denied.

In a prepared opening statement, Carper acknowledged questions surrounding "Director Mayorkas' qualifications."

"At this point in time, we do not have all the facts," Carper said. He also said that it's "my understanding" that Mayorkas has not yet been interviewed by the IG's office. He added that despite objections from Republicans, including Coburn, "This hearing will allow us to continue the process of vetting this nominee."

Aside from the controversy surrounding Mayorkas, Carper expressed confidence in his nomination.

"I have also taken the opportunity to review Mr. Mayorkas' FBI file, not once, but twice. Nothing in my conversations with Mr. Mayorkas or in my review of his FBI file has convinced me that we should not be holding this hearing today," Carper said.

According to the IG's office email to lawmakers, the FBI's Washington Field Office was told about the Mayorkas investigation in June after it inquired about Mayorkas as part of the White House background investigation for his nomination.

The investigation does not appear to have any direct ties to Clinton's tenure as secretary of state. Nonetheless, any hint of scandal or even the most tangential connection to Clinton, who is a possible 2016 Democratic presidential candidate, is likely to become fodder for Republican super PACs, which have sought to discredit her record while she maintains a lower profile with private speeches and work on a new book.

The nomination took on new importance earlier this month when Homeland Security Secretary Janet Napolitano announced she would be leaving the department, among the government's largest with 240,00 employees, in September to take over as president of the University of California.

Should Mayorkas be approved by the Senate, he almost certainly would lead the department until a permanent replacement for Napolitano was named. His promotion also would create a new leadership vacancy in a department already facing a leadership vacuum. With Napolitano's departure, 15 of the department's 45 top positions will either be filled with an acting official or be vacant altogether.

The Associated Press contributed to this report.