President Barack Obama and Russian President Dmitry Medvedev talked in detail this weekend about the negotiations and agreed to extend the talks, according to the statement.
An Obama administration official confirmed the two presidents spoke by telephone Saturday about the negotiations, but offered no further details. The official spoke on condition of anonymity because the administration had not announced the discussion publicly.
The Strategic Arms Reduction Treaty, known as START, expired Dec. 5. Both governments have spent several months negotiating a new pact that would further reduce the size of the nuclear arsenals on both sides.
White House press secretary Robert Gibbs said this past week that the two sides are making progress.
The Kremlin statement said the two presidents "continued a detailed exchange of opinions about the results achieved and the prospects of completing work on a document that is of vital importance for strategic stability in the world."
Medvedev and Obama "noted with satisfaction that the work of the delegations of both countries in Geneva has an intense and purposeful character that makes it possible to speak of substantial progress in the negotiation process," the statement continued.
The leaders "agreed to tell the negotiators to continue their energetic work without lowering the level and pace of cooperation with the goal of reaching final agreement on all issues," the statement said.
The expired START treaty, signed by then-Soviet President Mikhail Gorbachev and President George H.W. Bush, required each country to cut its nuclear warheads by at least one-fourth, to about 6,000, and to implement procedures for verifying that each side was sticking to the agreement.
Obama and Medvedev agreed at a Moscow summit in July to cut the number of nuclear warheads each possesses to between 1,500 and 1,675 within seven years as part of a broad new treaty.
Meanwhile, The New York Times has reported that, after years of rejecting Moscow's overtures, Washington is engaged in talks to limit the military use of cyberspace, and to strengthen Internet security.
With Internet-based attacks on computer systems (including government, military and corporate networks) increasing - and with President Obama due to name an official tasked with coordinating a national policy on Internet security - the two countries and a U.N. arms control committee are talking about the approaches needed against cyberweapons.
The U.S. has in past resisted Russia's call for an international treaty, similar to treaties governing nuclear, biological and chemical weapons. But now, discussions between the two countries have progressed.
"In the last months there are more signs of building better cooperation between the U.S. and Russia," Veni Markovski, an Internet expert and representative to Russia for ICANN, told The Times.