WASHINGTON — The White House has given the FBI permission to expand its probe of Brett Kavanaugh at least slightly, according to two people familiar with the matter, after facing a barrage of criticism over the weekend about the constricted investigation.

The FBI has completed an initial round of interviews as part of its reopened background check of the Supreme Court nominee, and more are likely in the coming days, people familiar with the matter said.

The White House and the FBI, though, still view the investigation as limited and time-sensitive, and Senate Majority Leader Mitch McConnell, R-Ky., said Monday he intends to hold a vote on the nomination “this week.”

Although the precise parameters of the expanded probe remained unclear Monday, this much was certain: No move by the White House is likely to quell the partisan fires raging in Washington. Republicans charged that Democrats were trying to delay the process to upend Kavanaugh’s nomination, while Democrats countered that the FBI’s investigation seemed to be a sham meant to support his eventual confirmation.

Even the broadened probe – which will now encompass the allegations of a third accuser – seemed to have limits that might fuel the controversy.

The FBI will not, for example, conduct an unfettered review of Kavanaugh’s youthful drinking or examine statements Kavanaugh made about his alcohol consumption during a Senate Judiciary Committee hearing to see if those answers were accurate or misleading, the people familiar with the matter said. The White House also could resist inquiries into new allegations, the people said.

But people familiar with the matter said agents will be allowed to question more witnesses with information on the sexual misconduct allegations. Drinking is inextricably intertwined with the allegations Kavanaugh faces, so it would be impossible to avoid that topic entirely. Two people familiar with the interviews so far say agents have asked routine questions, including about alcohol use.

Precisely who FBI agents will talk to was not immediately clear. A person familiar with the matter said the White House is being briefed regularly on the investigation. The people spoke on the condition of anonymity to discuss a sensitive and politically charged law enforcement matter.

The parameters being imposed on the bureau’s work are not completely abnormal because the investigation is a background check, rather than a criminal probe. In that context, the FBI functions as a contractor for the White House tasked with providing information on a nominee rather than an independent, investigative agency seeking to explore a possible crime.

But this particular background check is unusual in many ways – because it is being done after rather than before hearings, in semipublic view, and amid a raging debate about Kavanaugh’s character. The parameters of the FBI’s work have been dictated largely by the demands that three wavering Republican senators have made on the White House for more information about the allegations made against Kavanaugh, according to one person familiar with the work.

As of Monday afternoon, the bureau had conducted interviews with at least four people. Three of them were identified as attendees of a party in Maryland where Christine Blasey Ford alleged that Kavanaugh assaulted her when both were teenagers. The fourth was Deborah Ramirez, who had told the New Yorker that Kavanaugh exposed his penis to her when both were students at Yale.

Agents had not yet talked to Ford directly, a person familiar with the matter said, though she did testify publicly about her allegations at a Senate Judiciary Committee hearing.

On Monday, Democrats on the Judiciary Committee sent a letter to the FBI and White House that listed more than two dozen people they would like to see contacted.

Republicans, meanwhile, charged that their political rivals were merely trying to prolong the process in hopes of killing Kavanaugh’s chances of becoming a justice. Their position is precarious. Leadership has yet to lock down the 50 Republican votes needed to install Kavanaugh to the Supreme Court, and each passing day brings the possibility of new revelations.

“The time for endless delay and obstruction has come to a close. Judge Kavanaugh’s nomination is out of committee. We’re considering it here on the floor,” McConnell said Monday. “We’ll be voting this week.”

If nothing comes up that craters support for Kavanaugh, McConnell would plan to schedule the first test vote on the nominee Friday, with a final confirmation vote possible over the weekend. If the FBI completes its review earlier, McConnell might speed up that timeline.

Republican Sens. Lisa Murkowski of Alaska, Susan Collins of Maine and Jeff Flake of Arizona – considered key swing votes – had yet to announce how they would vote after the FBI completes its work.

Flake said he hoped the FBI would do a “real investigation,” rather than one meant to support a decision that Republicans already have reached.

Murkowski said Monday evening: “I am not going to prejudge. I’m going to see what they come back with.”

People familiar with the matter said the FBI already had talked to three people whom Ford identified as being at the party where she claims she was attacked: Mark Judge, Patrick J. Smyth and Leland Keyser.

Each has said previously they do not recall the gathering that Ford described. Eric Bruce, Smyth’s attorney, issued a statement Monday saying Smyth “truthfully answered every question the FBI asked him and, consistent with the information he previously provided to the Senate Judiciary Committee, he indicated that he has no knowledge of the small party or gathering described by Dr. Christine Blasey Ford, nor does he have any knowledge of the allegations of improper conduct she has leveled against Brett Kavanaugh.”

An administration official said the FBI now also would be allowed to investigate the claims of a third woman: Julie Swetnick.

Swetnick, who is represented by prominent Trump critic Michael Avenatti, said in a declaration that Kavanaugh was physically abusive toward girls in high school and at a house party in 1982 where she says she was the victim of a gang rape. Avenatti, who also represents a woman who claims she had an extramarital affair with Trump, said Monday that the FBI had not yet contacted Swetnick.

For his part, Trump said Monday he was open to a “very comprehensive investigation,” but suggested at different points that the probe would be guided by the wishes of Republican senators and that the FBI could decide whom to interview so long as it was “within reason.”

“I want them to do a very comprehensive investigation, whatever that means according to the senators and the Republicans and the Republican majority,” Trump said at a news conference. “I’m guided by the Senate. I want to make the Senate happy.”

Trump stressed that he wants the FBI to move quickly and that he continues to stand by his Supreme Court nominee, praising him for living “an exemplary life” and lamenting the effect of the national attention on Kavanaugh’s wife and children.

Privately, though, advisers say Trump was not happy that Kavanaugh talked so extensively about his drinking at the Senate Judiciary Committee hearing to consider the allegations against him. At the news conference, Trump somewhat undercut his own nominee, suggesting Kavanaugh had acknowledged “difficulty” with alcohol and noting how frequently he had referenced beer.

The Supreme Court, meanwhile, began its term Monday with two oral arguments – and an empty spot at the right end of the bench