According to his spokesman, he said anyone held responsible for separatist moves should be punished.
His comments echo those of some MPs who have voiced fears that Ukraine could split because of anger in the east and south at recent events.
Residents of the Crimean port of Sevastopol have been signing up as volunteers for self-defence and pro-Russian groups, fearing potential attacks by Ukrainian extremists.
Protesters on the southern peninsula have staged rallies against Ukraine’s new leaders and a Russian-speaking mayor has been appointed in Sevastopol, where Russia’s Black Sea fleet is based.
Some 20,000 people turned out at another rally in the city on Monday, chanting “Russia” as they called for secession from Ukraine.
The previous day saw an even bigger demonstration.
Almost 60 percent of the region’s population are ethnic Russians.
Russian MPs visiting Sevastopol met residents and denied reports that Russian passports would be given to all Ukrainians who apply.
Sergei Mironov, head of a pro-Kremlin party’s parliamentary faction, said those Ukrainians who wanted Russian citizenship should be given passports as quickly as possible.
“The geopolitical struggle for Ukraine should not come to resettling the population (of Ukraine) to Russia by giving them Russian passports. This would be the greatest mistake and even a tragedy for Russia,” Crimean human rights activist Olga Timofeyeva told the delegation from Moscow.
A senior figure in the Russian Duma acknowledged that such a sensitive move would inflame Kiev.
“This is a very sensitive issue. It has to be worked on by a number of federal departments. This has to be decided by the highest authorities in Russia. And of course we should understand that if such proposals are legally approved in Russia the reaction of Kiev will be very negative. We can’t do anything which could provoke armed response and bloodshed with respect to primarily and including our compatriots,” said deputy chairman of Russian Duma foreign affairs committee Leonid Slutsky.
But moves are afoot in Crimea to challenge the authority of whatever new national government is formed.
An extraordinary session of the Crimean Rada – the region’s parliament – is due to be held on Wednesday.
Its speaker has said it will not recognise new decisions of the national parliament in Kiev.