WASHINGTON — The Pentagon is moving to ease the pain of mandatory, unpaid furloughs that civilian employees have had to bear for a month because of budgetary pressures, cutting the number of days off from 11 to six, The Associated Press has learned.

Officials say the Pentagon found sufficient savings in the final months of the current fiscal year to lessen the burden on those who have had to take a day off a week without pay since early July. Officials said last week that they would need to find about $900 million in savings in order to eliminate five of the 11 furlough days.

Defense Secretary Chuck Hagel approved the final numbers this week after meeting with top leaders. The decision came as about 650,000 civilian workers began their fifth week of furloughs, which have riled department employees and prompted many to complain directly to Hagel during his recent visits to military bases.

Hagel has been saying that budget officials were trying to find savings to shorten the furlough time. But officials also have cautioned that the savings are for this year only if Congress doesn’t act to avoid automatic, across-the-board cuts slated for next year.

The 11 furlough days were expected to save roughly $2 billion.

Officials said the savings are the result of a number of things, including penny-pinching by the military services and Congress’ decision to give the Pentagon more flexibility in moving money around among accounts.

Facing $37 billion in budget cuts this year, Pentagon leaders initially announced the 11 furlough days, arguing they needed to shift money to other priorities, including combat training, flight hours, and efforts to bring tons of equipment out of Afghanistan. Since then, budget chiefs have been analyzing the numbers in a persistent effort to find unspent dollars as they neared the end of the fiscal year.

A law enacted two years ago ordered the government to come up with $1.2 trillion in savings over a decade. The law included the threat of annual automatic cuts as a way of forcing lawmakers to reach a deal, but they have been unable to do so. The Pentagon, as a result, is facing $500 billion in cuts over the next decade.

For the 2014 budget year, that will mean a reduction of up to $54 billion from current spending totals.

About 85 percent of the department’s civilians have been subject to furloughs.

The bulk of the exempt employees are foreign nationals or workers not paid through appropriated funding. Nearly 7,000 defense intelligence workers are also exempt, along with about 29,000 workers at Navy shipyards, where officials worried that the harm to shop maintenance would end up costing more than the salary cuts would save.