VATICAN CITY — Pope Francis encouraged Russian President Vladimir Putin to engage in "sincere" international efforts aimed at bringing peace to Ukraine as the two men met privately at the Vatican Wednesday.

Earlier in the day, the U.S. ambassador to the Holy See, Kenneth Hackett, said his country would like to see the Vatican step up its concern about what is happening in Ukraine during the pope's meeting with Putin, the second time the Russian leader and Francis have met since the pontiff was elected in 2013.

While Francis has deplored the loss of life in Ukraine and called on all sides to respect what has proven to be a shaky cease-fire, he hasn't publicly put any blame on Russia in an apparent bid not to upset the Holy See's delicate and often thorny relations with the Orthodox Church in Russia, where Catholics are a tiny minority.

"We think they could say something more about concern of territorial integrity, those types of issues," Hackett told reporters. "It does seem that Russia is supporting the insurgents. And it does seem that there are Russian troops inside Ukraine."

During the few minutes that Putin and Francis greeted each other and took their leave before and after their 50-minute-long closed door talks, there was no mention of any blame regarding Ukraine, although the protracted hostilities in that Eastern European nation bordering Russia was a main thrust of the discussion.

"As it was possible to predict in the context of the world situation, the talks were dedicated principally to the conflict in Ukraine and the situation in the Middle East," said a Vatican spokesman, the Rev. Federico Lombardi.

The Holy See is highly worried about the fate of the Christian minority in the Middle East.

Putin and Francis seemed eager to start their talks, which began quite tardily. Pulling into a Vatican courtyard in a black stretch limousine, Putin arrived an hour and 20 minutes late, after flying to Rome from Milan, where he spent the morning touring the Russian pavilion at the world's fair and meeting with Italian Premier Matteo Renzi.

Despite Putin's delay, a rare breach of protocol for VIPs paying a call on the pope, Francis greeted him cordially in German, a language the Russian knows well from his secret service days. Putin nodded silently in acknowledgement.

In their talks about Ukraine, Lombardi said, Francis stressed the "need to commit oneself in a sincere and great effort to achieve peace." Lombardi said both men "agreed on the importance of reconstructing a climate of dialogue and that all sides commit oneself to implementing the Minsk accords."

Francis also stressed that all sides work toward easing the tensions in the regions.

As he has done with other VIP visitors, the pontiff presented Putin with a medallion depicting an "angel of peace," who, Francis told the Russian, "conquers all wars and evokes the solidarity among peoples."

Putin gave the pope a depiction, embroidered with gold filament, of a church which had been destroyed in the Soviet era and later reconstructed.

"It was a great pleasure, an honor to meet you," Putin told Francis as he took his leave.

In Milan, Renzi heaped praise on Russia, calling it a crucial player in international anti-terrorism efforts, as the Italian premier sought Putin's help in ending the conflict in Libya that has fueled the Mediterranean migrant crisis.

Renzi didn't voice any criticism against the country's actions in Ukraine, saying simply that they both agreed there must be full implementation of the Minsk peace accord. Putin for his part stressed the price Italian businesses are paying for the economic sanctions lodged by the European Union against Russia, which annexed Crimea from Ukraine during the conflict.

Because of the Ukraine crisis, the leaders of the world's industrialized democracies for a second year in a row refused to let Putin join their G-7 summit. At the summit this month, they said sanctions against Russia won't be lifted until Moscow fully implements its part of the Ukraine peace accord, and could be increased if needed.

Russia accuses Ukraine of failing to launch political dialogue with the rebellious east and of keeping its economic blockade of areas controlled by pro-Russian rebels. Kiev, the United States, NATO and European leaders have blamed Moscow for supplying rebels with manpower, training and weapons. Russia denies the claims.

Hackett, the U.S. ambassador, noted that Putin has spoken about the plight of Christians.

Lombardi said Putin and Francis discussed the conflicts in the Middle East, notably in Iraq and Syria, a country where Moscow long held influence. The Vatican statement cited the "urgency" with which the international community must pursue peace efforts, "assuring at the same time the necessary conditions for the life of all components of society, including religious minorities and in particular Christians."

Ending his long day, Putin took off his dark suit jacket and got together with his old friend, ex-Premier Silvio Berlusconi. Berlusconi gave him a warm hug and two large bottles of unspecified content in an encounter at Rome's main airport, where the Russian was to board a jet to return to Moscow, according to the Italian news agency ANSA.

(This story has been corrected to show Hackett spoke Wednesday, not Tuesday.) Winfield reported from Rome. Trisha Thomas contributed from Milan. Vladimir Isachenkov contributed from Moscow and Frances D'Emilio contributed from Vatican City.