Moscow (CNN) There aren't many world leaders prepared to keep the Pope hanging around for a meeting. Russia's President is perhaps the only one.

Pope Francis discovered this on Wednesday as he waited , patiently, for more than an hour at the Vatican for his guest to finally arrive.

There aren't many world leaders either who could annex one part of a neighboring country while backing a bloody rebellion in another part, and still avoid strong criticism from, arguably, the world's most influential religious figure.

Vladimir Putin appears to fall into that narrow category too.

The issue of Ukraine was raised, we're told, during their brief, closed-door meeting. According to a Vatican statement, "The Holy Father affirmed that it is necessary to make a sincere and great effort to forge peace," in the war-ravaged country.

Pope Francis and Putin also agreed to "restore a climate of dialogue."

But the exchange was not the condemnation called for by many, including members of the Greek Catholic congregation, who number millions in Ukraine, and who have expressed frustration at the Pope's failure to criticize Russia's role in the Ukraine conflict.

Nor are the words likely to satisfy the U.S. Ambassador to the Holy See, Kenneth Hackett, who urged the Vatican, ahead of the Putin meeting, to "say more about concerns on territorial integrity" in Ukraine.

To be fair, the Vatican is not following the same diplomatic agenda as Western governments regarding Russia.

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The current Pope in particular has forged an unlikely strategic alliance with the former KGB officer-turned President that transcends the political tensions felt elsewhere with the Kremlin.

The partnership seems to have begun in September 2013 when Pope Francis and Putin urged the U.S. to desist from taking military action in Syria -- a strong Kremlin ally.

According to Christopher Hale, executive Director of Catholics in Alliance for the Common Good, writing in Time Magazine , "Francis and Putin used two very different means to communicate their messages: Francis held a worldwide prayer vigil for peace, while Putin penned a somewhat audacious editorial in The New York Times in which he cited Pope Francis's objection as a reason for the U.S. to not get involved in the region."

Pope Francis meets Russian President Vladimir Putin at the Vatican.

Hale goes on to suggest that Francis may play a diplomatic role in resolving the conflict in Ukraine too.

But if Wednesday's meeting was anything to go on, in which the Pontiff and the President exchanged gifts, I wouldn't get your hopes up.

No, that meeting was more about Putin than the Pope.

Just a day after being publicly scolded by the world's industrial powers, the G7 -- including a particularly strong rebuke from U.S. President Barack Obama -- Putin was shoulder to shoulder with the spiritual leader of 1 billion Roman Catholics worldwide.

Russia may not be quite so isolated after all.