President-elect Donald J. Trump’s Twitter post last week that the United States must “greatly strengthen and expand its nuclear capability” provoked confusion and anxiety that intensified the next day when he added, in a television interview, “Let it be an arms race. We will outmatch them at every pass and outlast them all.”

Largely unspoken in the tumult, but running just below the surface, was a deep uncertainty about the future of a cornerstone of America’s nuclear policy: its program to safeguard the nation’s atomic stockpile.

A central mission of the nation’s weapons laboratories is to ensure that the country’s nuclear weapons still work if needed. To do that, the government has long relied on a program that avoids the need for underground testing, instead using data from supercomputers and laboratory experiments and inspecting the warheads.

But some nuclear analysts say that the Trump administration is likely to face decisions that could upend the bomb program, leading to a resumption of testing and perhaps a new global arms race if they are mishandled. Adding to the concern is Mr. Trump’s choice of a politician with no expertise in nuclear or technical matters, former Gov. Rick Perry of Texas, to lead the Energy Department, which runs the nation’s nuclear-weapons labs and the safeguards program.