* Putin arrives late again for his third meeting with Pope Francis
* Putin calls talks "very substantive, interesting"
* Putin set to see Italian leaders afterwards in short trip (Adds more from meting, background)
By Philip Pullella
VATICAN CITY, July 4 (Reuters) - Russian President Vladimir Putin thanked Pope Francis for "very substantive" talks on Thursday, a day before Ukraine's Catholic leaders were due at the Vatican.
Putin, who has met with Francis twice before, arrived an hour late. He had been 50 minutes late for their first meeting in 2013 and more than an hour late for their second in 2015 - highly unusual for world leaders meeting the pope.
"Thank you for the time you have dedicated to me," Putin said at the end of 55 minutes of talks, helped by two interpreters.
"It was a very substantive, interesting discussion," he told the pope within earshot of reporters as they were exchanging gifts in the frescoed private papal study, which Francis uses only for official occasions.
A Vatican statement said the talks concentrated on the situations in Syria, Ukraine and Venezuela.
Putin and Russian Foreign Minister Sergey Lavrov, who did not join the talks, later held a separate meeting with the Vatican's secretary of state, Cardinal Pietro Parolin, and its foreign minister, Archbishop Paul Gallagher.
Francis gave Putin a signed copy of his peace message for this year and a large 18th century etching of St. Peter's Square, "so you don't forget Rome".
Putin gave the pope a DVD of a movie about the Renaissance master painter and sculptor Michelangelo by the Russian filmmaker Andrei Konchalovsky and a large painted Orthodox icon of the apostles Peter and Paul.
Putin is scheduled to see both the Italian president and prime minister later on, and is expected to return to Moscow in the evening after an official dinner.
Ukraine, which remains a bone of contention between the Vatican and Russia, was expected to be a main topic of the men's discussion, held in the official papal library in the Vatican's Apostolic Palace.
When they last met in 2015, the pope urged Putin to make a "sincere and great effort" to achieve peace in Ukraine and help bring an end to fighting between government forces and pro-Russian separatist rebels in the east.
TENSIONS IN UKRAINE
On Friday, leaders of Ukraine's Catholic Church begin two days of meetings at the Vatican to discuss various problems in their former Soviet republic.
The Ukrainian Orthodox Church, which had for centuries been effectively under the control of the Russian Orthodox Church, declared its independence and set up a national Church.
Putin has aligned himself closely with the Russian Orthodox Church and Moscow strongly opposed the move, saying it had been done for political rather than religious motives.
Three years ago, Francis held brief talks with Russian Orthodox Patriarch Kirill in Cuba -- the first such meeting in history and a landmark step in healing the 1,000-year-old rift between the Western and Eastern branches of Christianity.
The meeting took place amid speculation that Putin's visit could be a prelude to the first trip by a pope to Russia.
Mikhail Gorbachev, the last leader of the Soviet Union, and Boris Yeltsin, the first president of post-Soviet Russia, had invited the late Pope John Paul to visit.
But a trip was not possible because of tensions between the Vatican and the Russian Orthodox Church, the largest and most influential in world Orthodoxy, with 165 million of the world's 250 million Orthodox Christians.
Since meeting Kirill, Francis visited a number of countries with predominantly Orthodox populations, including, this year, Romania, Bulgaria and North Macedonia. (Reporting by Philip Pullella; editing by Diane Craft and Crispian Balmer)
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