It is the Russian president's first trip to a European Union country this year.
On Saturday Mr Putin and Patriarch Kirill of Moscow are visiting the Monastery of St Panteleimon, which is inhabited by Russian monks.
It is set in the 1,000-year-old Mount Athos autonomous monastic community, no women are allowed inside.
Patriarch Kirill of Moscow arrived in northern Greece on Friday for the visit.
Vladimir Putin is in Greece to discuss energy and privatisation deals with Greek Prime Minister Alexis Tsipras.
Russia is one of Greece's main trading partners, but business has been hit by sanctions against Russia and a drop in commodity prices.
Mr 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.
Speaking in Athens President Putin said: "These are difficult times for everyone - in terms of the economy and international security.
"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."
Greece wants to boost tourism from Russia after a slump in 2015, as well as attract interest from Russian companies in the planned privatisation of rail and other transport services.
