Earlier on Friday, Washington rejected Moscow's proposal to unconditionally extend New START, which expires in February, for one year and continue negotiations on the new pact to replace the only arms control regime between the two countries.
The US was also offering a one-year extension but in exchange for Russia capping the buildup of its nuclear arsenals, which is not covered by the original New START.
Billingslea claimed earlier this week that there is an agreement in principle at top political levels that needs "to percolate down" - only to be publicly disavowed by his Russian counterpart, Deputy Foreign Minister Sergey Ryabkov, who insisted that "huge differences" remain.
Russian Ambassador to the US Anatoly Antonov also told Newsweek magazine that Moscow sees a "deep crisis of confidence" in its relations with Washington.
The treaty - the only remaining arms control accord between the United States and Russia - is set to expire in February.