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A new audit of the government’s estimated spending to maintain its nuclear deterrent in the next decade concludes that the expenses will likely be at least tens of billions of dollars more than the Energy and Defense departments have claimed.

An unarmed Minuteman III intercontinental ballistic missile launches in February during an operational test from a facility on north Vandenberg Air Force Base. Joe Davila/U.S. Air Force

The report by the U.S. Government Accountability Office, a watchdog arm of Congress, is the second official rebuke in the past six months of a claim by Obama’s senior defense appointees a year ago that the likely expense would be $263.8 billion.

Last December, the Congressional Budget Office suggested in its own report that administration officials had undercounted likely nuclear-related expenses by around 66 percent. Its calculations pegged the 10-year costs related to preserving the nuclear deterrent at a total of $570 billion, large enough to make the 30-year government-wide total plausibly exceed $1 trillion.

The GAO, in a report released on June 10, did not estimate the exact size of the undercount. But it said the Pentagon had wrongly omitted from its formal estimate of nuclear-related work the projected costs of modernizing the U.S. ballistic missile and bomber forces, which the budget office has said may total $64 billion over the next decade.

Defense officials told GAO analysts that the cost of replacing Minuteman III ballistic missiles was not included in the administration’s calculus because the program is “not yet defined,” even though it’s in the department’s plans, the report said. “An Air Force official added that specific estimates for the new bomber were considered too sensitive to include in the report.”

GAO found those explanations wanting, and said the Defense Department should have included a range of likely expenses, even if the precise tallies cannot be forecast.

GAO also said the Energy Department, in the administration estimate last year, had included “less funding than will be needed” to fulfill its ambitious plans for modernizing a series of nuclear warheads, including those for ballistic and cruise missiles. It also said the department had projected billions of dollars in savings from efficiency improvements that it had not figured out how to achieve. In addition, the report said Energy officials had excluded the costs of refurbishing or replacing several laboratories designed for special work with nuclear materials.

“By not including preliminary estimates or ranges for these projects and programs, DOE underestimated the total anticipated cost and limited the utility” of the 2013 report, the GAO said.

The report also said officials had not been transparent enough about how the administration estimated the costs of modernizing command links to the nuclear force, and that as a result it could not assess the accuracy of that assessment.

The new administrator of DOE’s National Nuclear Security Administration, Frank G. Klotz, responded that his agency is now providing a sound range of cost estimates for its deterrent-related work. The assistant secretary of defense for nuclear programs, Andrew Weber, promised to do the same.

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R. Jeffrey Smith worked for 25 years in a series of key reporting and editorial roles at The Washington...