WASHINGTON (AP) -- Veterans would get specialized medical care from private doctors more easily under a bill the Senate approved Friday.

The measure relaxes a rule that makes getting specialized care from local doctors difficult for some veterans, especially those in rural areas. Senators approved the bill by voice vote as they rushed to wrap up legislative work before a weeklong Memorial Day recess.

The Senate bill would open up private care to veterans who live within 40 miles of a medical facility run by the Department of Veterans Affairs, so long as the VA site does not offer the care required.

Senators said the measure was needed because some veterans were unable to get federally paid medical care from private doctors under the new Veterans Choice Act. The law blocks veterans from getting private care if they live within 40 miles of a VA medical facility, even if the veteran needs specialized care that is farther away.

Lawmakers from both parties have criticized the 40-mile rule, which they say goes against their intention to put the needs of veterans ahead of all other concerns, including cost.

Sen. Jerry Moran, R-Kan., said the VA was deliberately interpreting the 40-mile rule to deny veterans needed care. The VA recently tweaked the rule so it measures 40 miles by driving distance, rather than in a straight line.

Moran, who sponsored the Senate bill, said it "puts the veteran first and provides the fix the VA says they need to make certain that veterans are not dismissed or forgotten just because of where they live."

Moran and other lawmakers have pressed for changes in recent months, after far fewer veterans than expected were receiving treatment offered under the Veterans Choice law. The law was adopted last year in response to a scandal over long wait times for veterans seeking health care and falsified records covering up the delays.

Sen. Johnny Isakson, R-Ga., chairman of the Senate Veterans Affairs Committee, said the change approved Friday would "ensure veterans can receive care outside of the VA health care system if they face geographic or travel burdens, have a medical condition that would impact their ability to travel or for other factors that may be determined by the VA."

VA officials have said they are sympathetic to lawmakers' concerns but have cautioned that the change could cost tens of billions of dollars a year.

The measure now goes to the House.