When being interviewed by the Echo of Moscow radio earlier in the day, the UN chief said if the two countries sign a new START treaty, it would be very important and positive for the upcoming Nuclear Security Summit slated for April 12-13, in Washington, and the Review Conference on the Nuclear Non-Proliferation Treaty in New York in May.
Hopefully the new START treaty will become a positive agreement, he added.
Later in the day when meeting with Medvedev, Ban reiterated his optimism.
"I expect and sincerely hope that you and U.S. President ( Barack) Obama will sign the START treaty as soon as possible," Ban told Medvedev.
In reply, Medvedev said "I hope so" in English.
Policy divergences or technical details
Despite rounds of negotiations, Russia and the United States failed to reach a pact before the original 1991 START expired in December last year.
The protracted talks thus aroused media speculation that policy divergences, particularly of those surrounding the U.S. plans for missile defense in Europe, had prevented the two side from clinching the deal.
Moscow has repeatedly demanded a link between missile defense and the offensive weapons cuts to be included in the new START treaty. But any document formally linking the two issues can hardly be ratified by the U.S. Senate, said the RIA Novosti news agency.
However, official statements concerning the dragged-on negotiations so far only mentioned technical minutes as stumbling blocks. At Thursday's press conference, neither Lavrov nor Clinton showed any signs of lingering disputes in this regard.
Ahead of her Moscow visit, Clinton told Russian magazine The New Times on Monday that the key challenge was to cut nuclear arms in a way that is verifiable but less costly and operationally complex than the expired 1991 START.
"It's a technically very complex treaty to accomplish. We share an interest in making real reductions in our strategic arsenals, and that is the most important point," she said.
Meanwhile Lavrov revealed on Tuesday that the date and venue for the signing of the new treaty remained undetermined. He also said the 20-page treaty with an extensive protocol attached is likely to be finalized in late March or early April.