On Wednesday, the Oklahoma Republican demanded the "immediate issuance of new guidance" on the exemption status for "our men and women in uniform, as well as the civilians and contractors who support them."
On Monday, President Obama signed the "Pay Our Military Act," which ensures U.S. service members will continue to receive regular paychecks, as well as the civilian employees deemed exempt from the shutdown.
That said, Inhofe wants that authority under the act to be expanded to "the broadest extent possible" to cover those furloughed Defense Department employees.
"America cannot afford to look weak on national security, especially in the 21st century when the threat of global terrorism is real and evolving," Inhofe said.
House Armed Services Committee member Rep. Mike Turner went a step further, calling upon the Pentagon and White House to bring back all 400,000 civilian workers.
"I am astonished the President is willing to use the Department of Defense civilian personnel and risk our national security as a bargaining chip," the Ohio Republican wrote in a letter to Obama on Wednesday.
The military pay legislation "clearly authorizes" the Pentagon to pay service members and civilians alike, according to Turner.
"There is no reason these men and women serving our country should have to suffer as a result of a political showdown," he added.
Turner's letter comes a day after House defense panel chief Rep. Buck McKeon (R-Calif.) issued the same demand in a letter to Defense Secretary Chuck Hagel.
“I believe the legislation provides you broad latitude and I encourage you to use it,” McKeon wrote, referring to the new military pay act.
McKeon's letter came after House Majority Leader John Boehner (R-Ohio) accused the White House of “using DOD workers to play political games.”
On Tuesday, Hagel said department leaders were exploring options to expand the list of civilian employees deemed necessary for day-to-day Pentagon operations.
But department officials have yet to provide an update on those options to McKeon or other members of Congress, according to a committee spokesman.