The Reagan administration says its new budget will contain enough money to run the nation's nuclear weapons plants safely, despite Energy Secretary John Herrington's warning of a $360 million shortfall that could lead to shutdowns.

Reagan's chief of staff, Kenneth N. Duberstein, said Sunday that "unobligated balances" found within the department will make it possible to bring the facilities into compliance with safety and environmental laws."Mr. Herrington suggested that he wanted some additional spending rather than going into the Energy Department resources and looking for some money, which we have done," Duberstein said in an appearance on NBC's "Meet The Press."

"The president has said consistently we won't operate any of these plants unless we can operate them in a safe manner," he said.

Herrington suggested in a Dec. 9 letter to Duberstein that the department might have to shut some of its plants unless the administration proposes more than the $12.9 billion planned for fiscal 1989.

"I must in good conscience advise you that the system will, in all likelihood, be operating beyond the bounds of acceptable risk," he wrote. Details of the letter were published in Sunday editions of The Washington Post.

If the department gives priority to production rather than upgrading safety at the plants, Herrington said in the letter, "then unresolved environmental and safety issues are likely to lead to further shutdowns in the weapons complex." He said "a significant increase in resources" is needed over the next five years or the government will risk compromising the country's ability to produce and maintain its nuclear weapons stockpile.

Herrington told Duberstein in his letter that the department would use the last of an emergency contingency fund to pay for $200 million in improvements at its Savannah River plant in South Carolina, which has been plagued with safety and environmental problems.

He also cited unforeseen expenses at Rocky Flats, a Denver area plutonium processing facility with hazardous waste problems that are jeopardizing its operation, in explaining the expected $360 million shortfall.

Duberstein said he had sent a response to Herrington. He did not indicate on the television program whether the unobligated money to which he referred was in the contingency fund or elsewhere, and did not say how much money had been found within the department.