"The issue of proliferation is one that really keeps us up at night, and should keep us up at night, whether it's North Korea or Iran, and on both fronts we're seeing movement in the positive direction," Jones said.
CBS News chief Washington correspondent Bob Schieffer asked Jones about a New York Times report out this morning which says that Iran has enough information to design and build a functional A-bomb.
"Whether they know how to do it or not is, you know, is a matter of some conjecture, but what we're watching is what is their intent. We have been worried about that intent," he said.
Iran is open to negotiations, according to Jones.
"We have two more meetings scheduled. One in which they will announce [that]... they will allow the inspectors to visit the site which has just been recently announced, and the other one to discuss methodology by which we can ship their enriched uranium out of the country. Those two things alone move the dial in our direction favorably."
Jones also said the debate over whether or not to send an additional 40,000 troops to Afghanistan continues, and that President Barack Obama should be presented with options. More U.S. combat troops is not a "fait accompli," Jones said.
"We've had one lengthy meeting already last week with General McChrystal on the screen from Kabul. We will have more. This week we'll have two more meetings. All of these things are being discussed as they should be against the backdrop of this unfortunate tragedy that we all regret," he said, in reference to the.
The general said the most important element of the discussion is to "make sure that the strategic issues and the strategic decisions that the president will make are fully aired and vetted, and that the options that the president has are also put on the table.
"It would be, I think, unfortunate if we let the discussion just be about troop strength. There is a minimum level that you have to have, that there's unfortunately no ceiling to it."
Schieffer asked Jones if he agreed with Gen. McChrystal that scaling back troops in Afghanistan would be a "short-sighted strategy."
"We [already] do have a strategy. What Gen. McChrystal has done is presented his opinion, is presenting his opinion of what he thinks his role is within that strategy. Our strategy is a regional strategy. We focus on Afghanistan and also Pakistan," Jones answered.
The moderator asked if the president's hands are tied since McChrystal is "the new man" he sent to oversee Afghanistan. But Jones insisted that the president has not formally received the request for additional troops, while also noting success in Pakistan.
"The relationship between the United States military and the Pakistani military is a growing one. It's on the ascendancy. We hope that will lead to a campaign against all insurgents on that side of the border. If that happens, that's a strategic shift that will spill over into Afghanistan."
Jones said that if the Taliban return to power, it does not necessarily mean that al Qaeda will be strengthened in the region, but "depends on the circumstances."
"I think the deliberation is important," he replied when questioned whether U.S. deliberations could be viewed as stalling by allies. "We have not only our national deliberation but we have an international presence that is extremely impressive and important. We are working side by side with NATO, for example, as we evaluate Gen. McChrystal's recommendation. So this is something that the president had said we would always do - back in March he said, after the [Afghan] elections we will make an assessment. This is exactly what's happening.
"No one has suggested that we're about to leave Afghanistan."
Jones would not speculate how long the White House deliberations will go on for.
"[W]e have time on the president's schedule. He's going to devote an enormous amount of his time to lead us through this. Everyone will be involved. And at the end of the day, the right way to do this is to present the president with a set of options on what he can do. Afghanistan will be the topic but it won't be the only topic. It will be Pakistan. It will be the region. That's the way we should do it."