"We proposed to the United States that we conclude a new, legally binding agreement to replace the START Treaty, which is set to expire on December 5, 2009," Medvedev, who is on a trip to the Netherlands, said in a declaration published on the Kremlin website.
"We are ready to reduce the number of strategic delivery vehicles by a significant factor vis-a-vis the provisions of the START-I Treaty," he said.
"With regard to the warheads, their number should be below the level established by the Moscow Treaty of 2002, as we have agreed with (U.S.) President Barack Obama," he said.
Meanwhile, "it is important to maintain the conditions set out in the START-I Treaty concerning the deployment of strategic offensive weapons exclusively on national territory," the president said.
Medvedev also stressed the existence of "serious problems that remain to be resolved."
"We cannot agree with U.S. plans to establish a global missile defense. I would like to emphasize that the reductions we are suggesting are possible only if the United States addresses Russian concerns. In any event, the problem of the relationship of strategic offensive and defensive weapons should be clearly laid out in the treaty," he said.
Another major concern, Medvedev noted, is the prospect of equipping strategic offensive weapons with non-nuclear warheads.
"Such weapons could be detrimental to strategic stability," he said.
Medvedev and Obama agreed at their first meeting in London in early April to negotiate a replacement for the START I by the end of the year.
The two sides held their first round of negotiations in Moscow on May 19-21, which was described as a "success."
The second round of talks were held in Geneva on June 1-3.
A follow up round of talks is scheduled on June 22 in Geneva, Medvedev's spokeswoman Natalya Timakova was quoted by local media as saying on Saturday.
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