The EU has accused Belarus of mounting a "hybrid attack" on it by flying in thousands of migrants, mainly from the Middle East, and pushing them to try to cross illegally into Poland.
The Kremlin has denied any Russian role in the crisis, but Putin offered to help resolve it on Sunday.
Asked on Monday how Russia saw itself contributing, Kremlin spokesman Dmitry Peskov said: "exclusively as a negotiating intermediary, which is partly (already) happening."
On a conference call with reporters, Peskov also dismissed as "wrong" a statement by the U.S. State Department that Belarus's actions on the border with the EU aimed to distract from Russian military activities close to Ukraine.
Ukraine has said there are nearly 100,000 Russian soldiers near its border and the United States has issued warnings over possible Russian aggression.
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