WASHINGTON D.C. -- Defense Secretary Ash Carter said Wednesday he is asking the Pentagon to suspend efforts to reclaim re-enlistment bonuses of thousands of California National Guard soldiers.

In a statement, Carter said not all soldiers given the bonuses knew they were ineligible to receive the erroneous payments. While there is “an established process in place by which service members can seek relief,” the defense secretary said the process for many has moved too slowly, which has led to “an unreasonable burdens on service members.”

“We will provide for a process that puts as little burden as possible on any soldier who received an improper payment through no fault of his or her own,” Carter said. “At the same time, it will respect our important obligation to the taxpayer.”

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White House spokesperson Josh Earnest said Wednesday that President Obama wants to be fair to all service members, including those who have tried to repay the bonuses.

After Carter’s announcment, California’s Senators Barbara Boxer and Dianne Feinstein said they would seek a “permanent solution” to the problem.

“When Congress returns after the election, we will introduce legislation to hold the Pentagon to its commitments,” the pair said in a joint statement. “The small number of service members who knew they weren’t supposed to receive bonuses will be exempt from the bill. We’re hopeful the Pentagon will resolve this issue on its own, but want to ensure those who wore our nation’s uniform that they won’t be punished for the actions of others.”

Prior to Carter’s announcement, the House Oversight Committee said Tuesday it has launched an investigation into the attempt to reclaim the re-enlistment bonuses.

The committee asked the Guard to turn over all documents and audits related to the decade-old payments of $15,000 or more to soldiers who agreed to re-enlist for the wars in Iraq and Afghanistan.

The National Guard has said the bonuses were wrongly paid but its effort to reclaim them from thousands of soldiers and veterans in California and across the country has caused public outcry, including widespread criticism from Congress.

Oversight Chairman Jason Chaffetz of Utah and three other Republicans said in a letter that officials who mismanaged the bonus programs must be “held accountable.” The lawmakers said Guard officials must turn over relevant documents by Nov. 7.

Maj. Gen. Matthew Beevers of the California National Guard said officials are working with Congress to approve legislation ordering the National Guard Bureau to clear the debts of soldiers who were wrongly told they were eligible for bonuses of $15,000 or more.

Col. Peter Cross, spokesman for the California National Guard, said Tuesday that about $22 million has been collected so far from fewer than 2,000 soldiers.

Other states may have been affected, but “California is where the majority of this occurred,” said National Guard Bureau spokeswoman Laura Ochoa.

Soldiers said they feel betrayed at having to repay the money.

“These bonuses were used to keep people in,” said Christopher Van Meter, a 42-year-old former Army captain and Iraq veteran who was awarded a Purple Heart. “People like me just got screwed.”

Van Meter said he refinanced his home mortgage to repay $25,000 in reenlistment bonuses and $21,000 in student loan repayments that the military says was improperly given to him.

Susan Haley, a Los Angeles native and former Army master sergeant who deployed to Afghanistan in 2008, said she feels betrayed. She said she sends the Pentagon $650 a month -- a quarter of her family’s income -- to pay down her debt to the military.

“They’ll get their money, but I want those years back,” said Haley, who served for six years.

The Pentagon demanded the soldiers repay their enlistment bonuses after audits revealed overpayments by the California National Guard under pressure to fill ranks and hit enlistment goals at the height of the two wars. If soldiers refused, they could have faced interest charges, wage garnishments and tax liens.