The nuclear initiative has been a signature issue for Mr. Obama: It is among the goals he campaigned on in 2008 and part of the reason he was awarded the Nobel Peace Prize barely a year into his presidency. Benjamin J. Rhodes, a deputy national security adviser, told reporters on Tuesday that the administration’s overall efforts had made it “harder than ever before for terrorists and bad actors to acquire nuclear material.”

But the administration’s budget for aiding global nuclear cleanups has been cut by half; some officials argue that less funding is needed with fewer nations willing to give up nuclear materials. A report Mr. Bunn helped write noted, “The administration is now projecting lower spending year after year for years to come, postponing or canceling a wide range of nuclear security activities that had been included in previous plans.”

In a recent report, the Nuclear Threat Initiative, a private advocacy group in Washington that tracks nuclear weapons and materials, warned that many radioactive sources were “poorly secured and vulnerable to theft.” The report called the probability of a terrorist’s detonating a dirty bomb “much higher than that of an improvised nuclear device.”

Ingredients for so-called dirty bombs, which use conventional explosives to spew radioactive material, are still scattered around the globe at thousands of hospitals and other sites that use the highly radioactive substances for industrial imaging and medical treatments. Less than half of the countries that attended the last nuclear summit in 2014 pledged to secure such materials, and they in turn represent less than 15 percent of the 168 nations belonging to the International Atomic Energy Agency.

Image Mr. Obama with Japan’s leader, Shinzo Abe, in 2014. Credit... Pool photo by Yves Herman

And while the administration succeeded in getting more than a dozen countries to give up their civilian stockpiles of highly enriched uranium, a main fuel of atomic bombs, the Nuclear Threat Initiative said in another report that some 25 nations still had such materials — enough for thousands of nuclear weapons.