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He arrived for the meeting along with his wife Melania, daughter Ivanka and son-in-law Jared Kushner. The meeting was keenly awaited as the two men have already clashed at a distance on issues including migration and climate change.
According to the BBC, Mr Trump is meeting Italy’s president and prime minister. Later, he will fly to Brussels for a Nato summit.
He earlier vowed to help Israelis and Palestinians achieve peace, as he ended the Middle East leg of his tour.
The US leader began his foreign trip with a two-day stop in Saudi Arabia over the weekend, urging Muslim countries to take the lead in combating radicalisation.
Mr Trump and his entourage arrived at the Vatican just before 08:30 local time; the meeting was arranged at the last minute which resulted in the early start time.
The US president was greeted by Archbishop Georg Ganswein, the head of the papal household, and escorted by the Swiss Guard from the Vatican courtyard to the offices of Pope Francis.
Journalists who covered the initial greeting said the pair were cordial with each other. Mr Trump told the Pope “it is a great honour”.
The two men spoke privately for about 20 minutes before returning to a public arena to exchange gifts.
Mr Trump followed his visit to the Vatican with talks with Italian President Sergio Mattarella at the Presidential Palace. Prime Minister Paolo Gentiloni will later join him at the US ambassador’s residence.
This is Mr Trump’s first visit to Europe since taking office in January.
Security has been stepped up across Rome, with the areas around the Vatican City, the Italian presidential palace and the American ambassador’s residence, where Mr Trump is staying, temporarily closed to traffic.
Despite the heavy police presence, about 100 anti-Trump protesters held a rally in one of Rome’s squares on Tuesday evening.
Later on Wednesday, Mr Trump will fly to Brussels, where significant protests are expected.
For the EU and for Nato, this visit is about damage limitation with the fervent hope of establishing some kind of transatlantic chemistry, the BBC’s Europe editor Katya Adler says.
She adds that the tone in Brussels has gone from off-the-record sneering when the erratic and unpredictable Mr Trump first won the November elections, to outright concern now that the implications of his presidency have begun to sink in.
Mr Trump will end his tour on the Italian island of Sicily at the G7 summit on Friday.
