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.

“We’ve seen a consistent, constant buildup in their inventory, but it hasn’t been a sudden rapid rise,” a senior American military official said. “We’re very, very well aware of what they’re doing.” White House officials share the assessment that the increase in actual weapons has been what one termed “slow and steady.”

But the bigger worry is the production of nuclear materials. Based on the latest estimates of the International Panel on Fissile Materials, an outside group that estimates worldwide nuclear production, experts say Pakistan has now produced enough material for 40 to 100 additional weapons, including a new class of plutonium bombs. If those estimates are correct — and some government officials regard them as high — it would put Pakistan on a par with long-established nuclear powers.

“If not now, Pakistan will soon have the fifth largest nuclear arsenal in the world, surpassing the United Kingdom,” said Bruce Riedel, a former C.I.A. officer and the author of “Deadly Embrace Pakistan, America, and the Future of Global Jihad.” “And judging by the new nuclear reactors that are coming online and the pace of production, Pakistan is on a course to be the fourth largest nuclear weapons state in the world, ahead of France,” he said. The United States, Russia and China are the three largest nuclear weapons states.

Mr. Riedel conducted the first review of Pakistan and Afghanistan policy for President Obama in early 2009.

Pakistan’s arsenal of deployed weapons is considered secure, a point the White House reiterated last week while declining to answer questions about its new estimates. The United States has spent more than $100 million helping the country build fences, install sensor systems and train personnel to handle the weapons. But senior officials remain deeply concerned that weapons-usable fuel, which is kept in laboratories and storage centers, is more vulnerable and could be diverted by insiders in Pakistan’s vast nuclear complex.

In State Department cables released by WikiLeaks late last year, Anne Patterson, then the American ambassador to Pakistan, wrote of concerns that nuclear material in Pakistan’s laboratories was vulnerable to slow theft from insiders. The cables also revealed an American effort to deny its ally technology that it could use to upgrade its arsenal to plutonium weapons.

“The biggest concern of major production, to my mind, is theft from the places where the material is being handled in bulk — the plants that produce it, convert it to metal, fabricate it into bomb parts, and so on,” said Matthew Bunn, a Harvard scholar who compiles an annual report called “Securing the Bomb” for the group Nuclear Threat Initiative. “All but one of the real thefts” of highly enriched uranium and plutonium, he said, “were insider thefts from bulk-handling facilities — that’s where you can squirrel a little bit away without the loss being detected.”

On Monday, The Washington Post, citing nongovernment analysts, said Pakistan’s nuclear arsenal now numbered more than 100 deployed weapons. In interviews over the past three weeks, government officials from several countries, including India, which has an interest in raising the alarm about Pakistani capability, provided glimpses of their own estimates. Almost all, however, said their real concern was not the weapons, but the increase in the production of material, especially plutonium. Pakistan is completing work on a large new plutonium production reactor, which will greatly increase its ability to produce a powerful new generation of weapons, but also defies Mr. Obama’s initiative to halt the production of weapons-grade material.

Nuclear projects are managed by the Pakistani military, but the country’s top civilian leaders are, on paper, part of the nuclear chain of command. Last year, Pakistan’s prime minister visited the new plutonium reactor at Kushab, suggesting at least some level of knowledge about the program. “We think the civilians are fully in the loop,” one senior Obama administration official said. Still, it is unclear how Pakistan is financing the new weapons production, at a time of extraordinary financial stress in the country. “What does Pakistan need with that many nuclear weapons, especially given the state of the country’s economy?” said one foreign official who is familiar with the country’s plans, but agreed to discuss the classified program if granted anonymity.

“The country already has more than enough weapons for an effective deterrent against India,” the official said. “This is just for the generals to say they have more than India.” American officials have been careful not to discuss Pakistan’s arsenal in public, for fear of further inflaming tensions and fueling Pakistani fears that the United States was figuring how to secure the weapons in an emergency, or a government collapse. But in November Mr. Obama’s top nuclear adviser, Gary Samore, criticized Pakistan for seeking to block talks on the Fissile Material Cutoff Treaty, which, if negotiated and adopted, could threaten Pakistan’s program.

In interviews last year, senior Pakistani officials said that they were infuriated by the deal Washington struck to provide civilian nuclear fuel to India, charging it had freed up India’s homemade fuel to produce new weapons. As a result, they said, they had no choice but to boost their own production and oppose any treaty that would cut into their ability to match India’s arsenal. In a statement in December, the Pakistan’s National Command Authority, which overseas the arsenal, said that it “rejects any effort to undermine its strategic deterrence,” adding, “Pakistan will not be a party to any approach that is prejudicial to its legitimate national security interests.”

Tommy Vietor, a spokesman for the National Security Council, said Friday that Mr. Obama remained “confident” about the security of Pakistani weapons, and said he “continues to encourage all nations to support the commencement of negotiations on the Fissile Material Cutoff Treaty.” Other officials say efforts are now under way to find a way to start negotiations in new forums, away from Pakistani influence. A senior Pakistani military officer declined Monday to confirm the size of his country’s nuclear arsenal or the describe rates of production, saying that information was classified.

“People are getting unduly concerned about the size of our stockpile,” said the officer, who was not authorized to speak publicly. “What we have is a credible, minimum nuclear deterrent. It’s a bare minimum.”