Putin has made only a handful of visits to EU countries since sanctions were imposed on Moscow two years ago in response to the Ukraine crisis.
Athens is keen to maintain its traditionally close ties with post-Soviet Russia, despite its participation in European Union sanctions against Moscow, and a gas pipeline project designed to limit Russia's regional energy dominance.
Russia is one of Greece's main trading partners, but business has been hit by the sanctions and a drop in commodity prices.
"We must examine these problems and look for a solution. It is not a coincidence that an opportunity for this has arisen in Greece a country with which we have deep and historic ties."
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Greece is also keen to reverse a slump in tourist arrivals from Russia last year, and attract interest from Russian companies in the planned privatization of rail and other transport services.
Greek Prime Minister Alexis Tsipras noted that Putin's visit comes just days after Athens reached a deal with eurozone bailout creditors to continue rescue loan payouts, under a deal that expands power of a state privatization committee.
Putin traveled to Greece with Russian Foreign Minister Sergey Lavrov and top executives from state oil and gas companies. Amid heavy security at Athens Airport, air force F-16s buzzed overhead as part of a welcoming ceremony.
"This will be the first time Putin has visited an EU country in the past six months and Russia-EU relations will be definitely on the agenda," said Alexander Kokcharov of the U.S.-based IHS Country Risk group.
"Putin is likely to offer investment projects in Greece, most likely in energy and transport sectors. However, we do not expect that Greece would go against the EU consensus.