President Obama took the opportunity Monday (Tuesday in South Korea time) to clarify his private comments that were picked up by TV microphones earlier in the day:

So this is not a matter of hiding the ball, I'm on the record. I made a speech about to a whole bunch of Korean unversity students yesterday. I want to see us over time, gradually, systematically, reduce the reliance on nuclear weapons. And as Dimitri said the United States and Russia, because of our history and because we are nuclear superpowers have a special obligation – that doesn't make it easier, because both countries are committed to their sovereignty and their defense.

And last point I'll make: the only way I get this stuff done is if I'm consulting with the Pentagon, if I'm consulting with Congress, if I've got bipartisan support, and frankly the current environment is not conducive to those kinds of thoughtful consultations. I think the stories you guys have been writing over the last 24 hours is probably pretty good evidence of that.