The announcement comes hours after the joint disarmament agreement expired on Thursday.
The dialogue is "an important factor for global stability and peace," the US European Command (EUCOM) said in a statement.
The agreement came after "productive and constructive progress" during peace talks in Abu Dhabi on Russia's war of aggression in Ukraine, which the United States mediated.
The news site Axios reports, citing "three sources with insight," that the two nuclear powers are approaching an agreement to continue to comply with New START despite the agreement having expired.
