But much of that effort has now petered out, and American officials have never been permitted to see how much of the money was spent, the facilities where the weapons are kept or even a tally of how many Pakistan has produced. The facility Pakistan was supposed to build to conduct its own training exercises is running years behind schedule.

Administration officials would not say if the subject would be raised during Mr. Zardari’s first meeting with Mr. Obama. But even if Mr. Obama raises the subject, it is not clear how fruitful the conversation might be.

Mr. Zardari heads the country’s National Command Authority, the mix of political, military and intelligence leaders responsible for its arsenal of 60 to 100 nuclear weapons. But in reality, his command and control over the weapons are considered tenuous at best; that power lies primarily in the hands of the army chief of staff, Gen. Ashfaq Parvez Kayani, the former director of Inter-Services Intelligence, the country’s intelligence agency.

For years the Pakistanis have waved away the recurring American concerns, with the head of nuclear security for the country, Gen. Khalid Kidwai, dismissing them as “overblown rhetoric.”

Americans who are experts on the Pakistani system worry about what they do not know. “For years I was concerned about the weapons materials in Pakistan, the materials in the laboratories,” said Rolf Mowatt-Larssen, who ran the Energy Department’s intelligence unit until January, and before that was a senior C.I.A. officer sent to Pakistan to determine whether nuclear technology had been passed to Osama bin Laden.

“I’m still worried about that, but with what we’re seeing, I’m growing more concerned about something going missing in transport,” said Mr. Mowatt-Larssen, who is now at Harvard’s Kennedy School of Government.

Several current officials said that they were worried that insurgents could try to provoke an incident that would prompt Pakistan to move the weapons, and perhaps use an insider with knowledge of the transportation schedule for weapons or materials to tip them off. That concern appeared to be what Secretary of State Hillary Rodham Clinton was hinting at in testimony 10 days ago before the House Appropriations Committee. Pakistan’s weapons, she noted, “are widely dispersed in the country.”