The Carl T. Hayden VA Medical Center in Phoenix. (Samantha Sais/Reuters)

The Senate on Wednesday overwhelmingly passed bipartisan legislation aimed at addressing the Department of Veterans Affairs’ scheduling crisis, capping a day that began with the FBI announcing that it will open a criminal investigation into the agency scandal.

FBI Director James B. Comey told lawmakers that the agency wants to help determine whether VA hospital administrators knowingly lied about wait times for veterans in order to receive performance bonuses.

The probe will be led by the FBI field office in Phoenix, where fraud allegations gave rise to a nationwide scandal.

The Senate’s 93 to 2 vote sends the measure to the House, which has passed its own bills.

Sponsored by Sens. Bernard Sanders (I-Vt.) and John McCain (R-Ariz.), the Senate bill would allow VA to do more contracting with private medical centers to meet demand for care and to shift $500 million within its budget to hire additional medical staff. It would also give the VA secretary greater power to fire or demote senior executives for poor performance.

The vote followed Tuesday’s passage of a stand-alone House bill that, like the Senate measure, would allow more contracting with private health providers. The House has also approved a VA firing measure, but it lacks a provision found in the Senate bill to ensure that fired or reprimanded officials can appeal.

Granting veterans greater access to private medical care could increase direct spending by about $35 billion over the next 10 years, according to a report Wednesday by the nonpartisan Congressional Budget Office.

The CBO report also says improved access could cause more veterans to seek care through VA, with the possibility of an additional annual cost of $50 billion.

“One of the costs of war is taking care of the men and women who fought in those wars,” said Sanders, who heads the Senate Veterans Affairs Committee. “If anyone disagrees . . . they shouldn’t send them off to war in the first place.”

McCain said Wednesday that additional measures may be required. “There will be more efforts to fix this gaping wound in America’s conscience,” he said.

Wednesday’s vote moves the Senate bill to the House, where Rep. Jeff Miller (R-Fla.), who chairs the Veterans Affairs Committee, and Rep. Michael H. Michaud (Maine), the committee’s ranking Democrat, will take first crack at developing final legislation.

Sanders said he is confident that “we can bridge the differences and send the president a bill he can sign in the very near future.”

Miller agreed, saying, “I’m hopeful that both chambers of Congress can soon agree on a final package to send to the president’s desk.”

As for the criminal investigation, the Justice Department asked the FBI for assistance, responding, in part, to pressure from lawmakers. This week, VA’s Office of Inspector General said it had expanded its probe to 69 medical facilities and has contacted the Justice Department in cases in which there was possible criminal activity.

Comey, speaking before the House Judiciary Committee, did not provide details on the inquiry. A law enforcement official, speaking on the condition of anonymity because the investigation is ongoing, said federal prosecutors will work with FBI investigators to determine whether there is a basis for criminal charges.

Internal investigations by the inspector general and VA have concluded that schedulers throughout the VA system faced pressure from supervisors to make it appear that veterans were receiving care within 14 days.

In reality, veterans at many hospitals throughout the country were waiting months to see doctors. Hospital administrators’ bonuses and promotions were tied to their ability to hit the 14-day target.

Sloan Gibson, the interim head of VA, said this week that the 14-day goal was unrealistic, and he suggested that it may have spurred the fraudulent record-keeping. Gibson said he was getting rid of the goal, and he pledged a series of short-term reforms to ensure that veterans who had been stuck on waiting lists for months received immediate care.

Sari Horwitz contributed to this report.