Belarus has made clear it would not welcome a Russian base, but the former Soviet republic remains dependent on Moscow for credit and energy.
Putin ordered the Russian Defense Ministry, with the participation of the Russian Foreign Ministry, to hold talks with their Belarusian counterparts and sign the agreement that is reached.
Belarusian President Alexander Lukashenko has not commented on Putin's initiative. The two presidents met in the southern Russian city of Sochi yesterday.
Belarus is a desirable location for Russia because it borders Ukraine and three members of the European Union and NATO: Lithuania, Latvia and Poland.
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"Against the background of the Ukrainian crisis, the stationing of a permanent Russian military contingent in Belarus will upset the balance of forces and facilitate an increase in tension in the whole region," said analyst Valery Karbalevich.
As part of an effort to improve Belarus' relations with the West, Lukashenko has stayed neutral on the conflict in Ukraine between the Western-aligned government in Kiev and the Russia-backed separatists in the east.