WASHINGTON – The White House budget office is recalculating how to apply automatic spending cuts for a handful of agencies, freeing up almost $4 billion for the Pentagon and another $1 billion or so for other agencies like the Homeland Security Department and NASA.

Capitol Hill aides familiar with the White House changes say the administration has identified almost $5 billion in cuts that can be restored under its reading of the arcane budget rules governing the across-the-board cuts, known as sequestration.

The calculations differ from earlier ones because a partial-year funding bill was replaced in March with a more detailed measure. After administration number crunchers redid their math, they were able to restore about $5 billion of the scheduled $85 billion in automatic sequestration cuts under a complicated, previously unused mechanism that dates to a 1985 budget law.

The move comes amid increasing public pressure to find ways to lessen the impact of sequestration. Federal agencies are warning that the mandatory cuts could mean cutbacks in services. Last week, Congress passed and President Obama signed legislation giving the Federal Aviation Administration the ability to avoid furloughs that were causing flight delays by tapping money in other accounts.

The cuts officially began in March after Congress and Obama could not reach an agreement on a broader budget deal. The automatic cuts had been imposed under a hard-fought 2011 debt and budget pact. They require a 5 percent cut to domestic agency operating budgets and an 8 percent cut to the Pentagon. Social Security was exempted and cuts to Medicare were limited to a 2 percent cut to health care providers. Safety net programs such as Medicaid, food stamps and school lunches for the poor were also exempted.

The cuts have so far failed to live up to the dire warnings issued earlier by agencies, in part because agency budget officers working with Congress have been permitted to transfer money between accounts.

But budget experts warn that the grip of sequestration will grow tighter as weeks and months pass, leading to teacher layoffs, reduced funding for infrastructure and economic development projects.

Many liberal activists were infuriated when Congress last week swiftly moved to address problems with air traffic control that led to widespread flight delays while leaving other problems such as cuts to preschool for the poor and Meals on Wheels for the elderly unaddressed. Most lawmakers are frequent fliers.

At issue in the latest recalculation are accounts that were cut more deeply under a full-year funding bill enacted in March than they would have been under the across-the-board cuts. They get funds restored. It’s up to the White House Office of Management and Budget to calculate the across-the-board cuts.

The recalculation surprised many people on Capitol Hill, but Republicans atop the budget committees declined to criticize the move. Republicans like Sen. John McCain of Arizona have sought to reverse cuts to the Pentagon — and it benefits the most from the new math.

The State Department was a big winner and said Friday that it would be able to avoid furloughing workers, in part because of the new calculations.

Meanwhile, the Food and Drug Administration said Friday that it would not have to curtail inspections of food processing plants. It had earlier warned that 2,100 plant inspections would have been canceled.