WASHINGTON  New American intelligence assessments have concluded that Pakistan has steadily expanded its nuclear arsenal since President Obama came to office, and that it is building the capability to surge ahead in the production of nuclear-weapons material, putting it on a path to overtake Britain as the world’s fifth largest nuclear weapons power.

For the Obama administration, the assessment poses a direct challenge to a central element of the president’s national security strategy, the reduction of nuclear stockpiles around the world. Pakistan’s determination to add considerably to its arsenal  mostly to deter India  has also become yet another irritant in its often testy relationship with Washington, particularly as Pakistan seeks to block Mr. Obama’s renewed efforts to negotiate a global treaty that would ban the production of new nuclear material.

The United States keeps its estimates of foreign nuclear weapons stockpiles secret, and Pakistan goes to great lengths to hide both the number and location of its weapons. It is particularly wary of the United States, which Pakistan’s military fears has plans to seize the arsenal if it was judged to be at risk of falling into the hands of extremists. Such secrecy makes accurate estimates difficult.

But the most recent estimates, according to officials and outsiders familiar with the American assessments, suggest that the number of deployed weapons now ranges from the mid-90s to more than 110. When Mr. Obama came to office, his aides were told that the arsenal “was in the mid-to-high 70s,” according to one official who had been briefed at the time, though estimates ranged from 60 to 90.