Price noted that de-escalation would mean Russian "troops returning to their barracks" and heavy weaponry returning to its regular storage locations."
He stressed that any legitimate exercises taking place in Russia should be transparent.
These exercises must either be explained or come to a halt and, Price stressed.
As reported earlier, the American and Russian delegations concluded a one-day meeting in Geneva on Monday, aimed at a diplomatic search for ways to ease tensions in Europe.
The U.S. delegation rejected any possibility of curtailing NATO's open-door policy toward other nations, including Ukraine.