At the start of the meeting, Putin praised bilateral and trade relations and said Kocharian would soon visit Moscow.
"I would like to thank you for your attention to the Year of Russia in Armenia. And we will also expect you in Moscow soon, so we can together open the Year of Armenia in Russia," Putin said. "All of this proves that our relations are developing intensively in all areas and our trade is growing."
Russian officials had earlier said the Armenian president was expected in Moscow in January.
Putin's talks with Kocharian are expected to focus on natural gas prices.
Russia's state-controlled Gazprom natural gas monopoly has announced plans to raise prices for deliveries to CIS countries. It is proposing to charge Armenia $110 per 1,000 cubic meters of gas, compared with a current $56.