WASHINGTON — Responding to pressure from Congress and veterans groups, the Department of Veterans Affairs said Tuesday it is relaxing a rule that makes it hard for some veterans in rural areas to prove they live at least 40 miles from a VA health site.

The change comes amid complaints from lawmakers and advocates who said the VA's current policy has prevented thousands of veterans from taking advantage of a new law intended to allow veterans in remote areas to gain access to federally paid medical care from local doctors.

The VA said it will now measure the 40-mile trip by driving miles as calculated by Google maps or other sites, rather than as the crow flies, as currently interpreted. The rule change is expected to roughly double the number of veterans eligible for the VA's new "Choice Card" program. The change could add billions of dollars in annual costs as tens of thousands of new veterans receive private medical care, which typically costs more than traditional care at VA hospitals and clinics.

"We've determined that changing the distance calculation will help ensure more veterans have access to care when and where they want it," Veterans Affairs Secretary Robert McDonald said in a statement.

Lawmakers from both parties had pressed for the change in recent months as it became clear that far fewer veterans than expected were taking advantage of a landmark law adopted last year to make it easier for veterans to get private care paid for by the government. The law was passed in response to a scandal over long wait times for veterans seeking health care and falsified records covering up the delays.

"Veterans deserve the highest-quality health care and should not be denied this right simply because of where they live," Sens. Johnny Isakson, R-Ga., and Richard Blumenthal, D-Conn., said in a joint statement. "We are pleased that Secretary McDonald is responding directly to concerns voiced by the Senate Veterans Affairs Committee and other members of Congress to ensure those reforms are working for all veterans."

Isakson chairs the Senate veterans panel, while Blumenthal is the panel's top Democrat.

Deputy VA Secretary Sloan Gibson said the 40-mile rule was implemented to comply with what officials believed was the intent of Congress in adopting the VA overhaul last year. "Based on feedback from veterans and members (of Congress), we believe we need to change it," he told the Senate panel.

"If you are looking for someone to hold accountable for the driving distance (rule), I'm the guy," Gibson said.

Moments later, however, Gibson read aloud from the law, which says that in calculating the distance from a nearest VA medical facility, Congress expected that "VA will use geodesic distance, or the shortest distance between two points."

Despite that language, Gibson said VA officials believe the rule change "will still be in the spirit of the law and allow improved access for veterans."

Blumenthal agreed, saying the change "relies on common sense rather than flying crows."

Sen. Jerry Moran, R-Kan., said the plan did not go far enough. The VA policy applies to any VA medical facility within 40 miles of a veteran's home, even if the veteran needs specialized care that is farther away.

"The VA is denying access the law was intended to offer and forcing veterans to choose between traveling hours to a VA medical facility, paying out of pocket or going without care altogether," Moran told Gibson. "Veterans are not being put first."

Gibson said he was sympathetic to Moran's concern, but said VA officials believe that allowing mileage calculations based on specialized care would require a change in the law. He cautioned that such a change could cost the VA tens of billions of dollars.

VA officials know the choice program "is not working as well for veterans as it should work," Gibson said, but they are working hard to improve it.

More than 46,000 medical appointments with private providers have been scheduled since the program went into effect in early November, Gibson said. That number is a small fraction of the 20 million VA appointments completed in the first three months of the fiscal year, including 3.3 million appointments with non-VA providers through other VA programs.

The VA will continue to focus on outreach efforts to increase awareness of the choice program, Gibson said.