Pope Francis has met President Vladimir Putin at the Vatican during the Russian leader's visit to Italy.

But the Vatican played down the visit.

By late evening on June 10 the only mention of the visit on the Vatican Information Service's official English language site was an announcement on the Pope's Audiences schedule.

It said, "This afternoon, he is scheduled to receive in audience Vladimir V. Putin, president of the Russian Federation, and entourage."

On its front page the Vatican Radio website headlined a story "Pope Francis meets with President of Argentina."

The Russian government site RT.com also made no inititial reference to Putin's meeting with the pontiff on its front page carrying a story headlines, "Putin visits Italy: Milan Expo, Pope & old pal Silvio," a reference to former Italian prime minister Silvio Berlusconi.

Before the meeting RT.com commented, "Pope Francis has been rejecting calls from the Ukrainian Catholic Church to condemn Russia over allegations that it's fueling aggression, and instead called on all parties involved to cease hostilities."

The independent Catholic News Agency reported that in the second meeting between Francis and Putin, the discussion focused on the current crises in both Ukraine and the Middle East.

Under Putin, Russia has annexed the Crimean peninsula from Ukraine; and according to the Ukrainian government and Western nations, Russian arms and soldiers are fighting alongside pro-Russian separatists in the east of the country, CNA reported.

Putin has denied the presence of Russian soldiers in Ukraine.

The news agency said that a June 10 communique from the Vatican revealed that Pope Francis stressed to Putin the need to "engage in a sincere and great effort to achieve peace" in the Ukrainian conflict.

Before the meeting Britain's Press Association reported that Putin would meet Prime Minister Matteo Renzi in Milan before heading to Rome for an audience with Pope Francis.

"While the Pope has deplored the loss of life in Ukraine and called for all sides to respect the cease-fire, he has not publicly placed any blame on Russia in an apparent bid to not upset Vatican relations with the Orthodox Church and in hopes of engaging Russia's help to confront the persecution of Christians in the Middle East, the Press Association commented in a report.

Pope Francis was encouraged by a top American diplomat to take a tougher stance against Putin before their meeting, The Guardian reported.

The Pope, a frequent critic of military action, has taken a cautious approach to criticism of Russia since its annexation of Crimea, and Kenneth Hackett, the U.S. ambassador to the Holy See, said the Vatican "could say more about concerns on territorial integrity."

"Maybe this is an opportunity for the Holy Father to privately raise those concerns," Hackett said. Pope Francis had "certainly" been made aware of the violence in Ukraine and was not unaware of the crisis, he added.

His comments, which were made in response to reporters' questions at a briefing on an unrelated matter, came hours before the Argentinian pontiff hosted Putin, in the first meeting between the two leaders since 2013.

Putin drove to the Vatican in a stretch limousine arriving more than an hour late for his meeting, after flying from Milan, where he had met Renzi earlier in the day.