Rumsfeld said other countries would be tempted to obtain nuclear weapons if North Korea and Iran become nuclear powers, which he said would also raise the risk that international terrorist groups will obtain them.
"There is at least a reasonable likelihood that some other countries will decide that they need to have nuclear weapons," he said in a speech to a military audience at Maxwell Air Force Base in Alabama.
"And ... in a relatively short period you could have two, four, six other countries decide that," he said.
The effect would be "exactly the opposite of what the international community wants to have happen," Rumsfeld said. "A lower nuclear threshold, more countries with nuclear weapons, a greater likelihood that one of the countries or more might transfer those weapons to a non-state entity."
Rumsfeld said a US-led effort to mount an international effort to track and interdict suspect shipments was unlikely to stop the spread of nuclear materials.
"There is so much moving around the world by land, sea and air it is practically impossible -- not impossible, but certainly it would take a lot of countries co-operating with a high degree of cohesion," he said.
"The only thing that would do it is a high degree of cohesiveness and co-operation on the part of the international community and that is something that has been lacking," he said.
Rumsfeld's comments came less than 10 days after North Korean detonated its first nuclear explosion and amid fears that a second test may be in the offing.

Copyright AFP (Agence France-Presse), 2006