His comments followed talks between US and Russian officials in Moscow, the Russian capital, last week to discuss the treaty.
The final details of the deal are to be discussed at a high-level meeting between the two countries in Geneva next month.
The Start treaty, signed just before the collapse of the Soviet Union, led to deep cuts in the Russian and US nuclear arsenals.
Although the treaty has expired, both countries have agreed to continue to honour its main provisions, until the completion and legal ratification of a successor treaty.
"It is crafty to speak of strategic nuclear forces without touching upon missile defence"
Dmitry Medvedev, Russia's president
The broad aim of the new treaty is to reduce the number of deployed warheads below the 1,700-2,200 allowed under Start.
Despite the latest progress on the treaty, Medvedev said Moscow remains concerned with US plans for a missile defence system in Europe.
He said the Kremlin "will definitely raise the issue" of the missile shield with its US negotiators once Start talks resume.
"It is crafty to speak of strategic nuclear forces without touching upon missile defence," the Itar-Tass news agency quoted him as saying.
"If nuclear missiles are launched, anti-missiles are too."
Controversial defence system
Barack Obama, the US president, announced last July plans to "reset" troubled US ties with Russia and two months later cancelled plans to deploy elements of a new US missile shield in eastern Europe, near Russia's borders.
Moscow had fiercely opposed those plans, pushed by George Bush, Obama's predecessor, and at first cautiously welcomed Washington's decision.
However, Obama made clear US intentions to continue work on a new missile defence system elsewhere.
Russia has long pushed for a link between offensive and defensive weapons in a new Start treaty, and such language was part of a joint declaration on disarmament by Medvedev and Obama after a Moscow summit in July.