Mr Medvedev's remarks were the most vocal Russian statement that Mr Assad's days could be numbered. But he reiterated calls for talks between the government and its foes and repeated Moscow's position that he must not be pushed out by external forces.
Russia has been Mr Assad's main ally in the 22-month-old Syrian conflict.
Meanwhile, any sign that Syria's grip on its chemical weapons is slipping as it battles armed rebels could trigger Israeli military strikes, Israel's vice premier said yesterday.
Silvan Shalom confirmed a media report that Prime Minister Benjamin Netanyahu had last week convened a meeting of security chiefs to discuss Syria and the state of its suspected chemical arsenal.
Israel and Nato countries say Syria has chemical warfare agents at four sites. Syria is cagey about whether it has these, but says if it had it would keep them secure and use them only to fend off foreign attack.
The Israeli meeting on Wednesday had not been publicly announced and was seen as unusual as it came while votes were being counted from Israel's parliamentary election, which Mr Netanyahu's party list won narrowly.
Mr Shalom told Israel's Army Radio that should Syria's chemical weapons fall into the hands of Lebanon's Hezbollah guerrillas or rebels battling forces loyal to Mr Assad, "It would dramatically change the capabilities of those organisations."
Such a development would be "a crossing of all red lines that would require a different approach, including even preventive operations," Mr Shalom said, alluding to military intervention for which Israeli generals have said plans have been readied.
"The concept, in principle, is that this [chemical weapons transfer] must not happen," he said. "The moment we begin to understand that such a thing is liable to happen, we will have to make decisions."