By Phil Stewart and Idrees Ali

BRUSSELS/WASHINGTON (Reuters) - U.S. Defense Secretary Ash Carter on Wednesday suspended a Pentagon order that California National Guardsmen repay thousands of dollars in enlistment bonuses and tuition assistance they had received by mistake more than a decade ago.

"While some soldiers knew or should have known they were ineligible for benefits they were claiming, many others did not," Carter, who is in Europe meeting with U.S. allies, said in a statement.

"This process has dragged on too long, for too many service members," he said. "Too many cases have languished without action. That's unfair to service members and to taxpayers."

Thousands of California National Guard troops had been ordered to repay enlistment bonuses - some of more than $15,000 - that were improperly given to them. The Los Angeles Times, which first reported on the bonuses last week, said audits revealed the California Guard had overpaid troops in order to entice them to join and meet enlistment targets.

The Obama administration has been criticized by some military families and Republicans - including presidential candidate Donald Trump - for not doing enough for veterans. There also have been bipartisan calls in the U.S. Congress to forgive the overpayments.

"The president has been pleased to see that in the last 24 hours the Department of Defense make specific commitments to ensuring that our service members are treated fairly," White House spokesman Josh Earnest said during a media briefing in Washington.

Carter, speaking to reporters in Brussels as he announced the suspension, said the law required the Pentagon keep open the option of someday again seeking repayment.

"But the point is that ... there won’t be any more collections until we put in place a process that can expeditiously and fairly deal with these issues," he said.

Senior Defense Department officials have been told to assess the bonus situation and establish a "streamlined, centralized process" by the start of next year, Carter said in the statement. He added that about 2,000 people had been asked to repay erroneous payments.

"The objective will be to complete the decision-making process on all cases as soon as possible - and no later than July 1," he said.

The streamlined process, which will build on existing processes, would evaluate each case individually, Peter Levine, acting undersecretary of defense for personnel and readiness, told reporters in Washington.

Levine said the amount of the improperly paid bonuses was unclear but a nationwide audit had found that the issue affected people outside California as well but the "numbers in other states are in the dozens, rather than the hundreds or the thousands."

"The process that we have allows us to correct our records and to correct our payment," he said. "We do not have the authority or the ability to go and change people's credit records."

U.S. House Speaker Paul Ryan said in a statement on Wednesday that Congress would "continue to work on any reforms necessary to ensure this doesn't happen again."

(Reporting by Phil Stewart; Additional reporting by Idrees Ali; Editing by Bill Trott)