US President Donald Trump has met Pope Francis at the Vatican for a short private audience on the third leg of his overseas trip.

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.

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.

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Much-anticipated meeting

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 gave the Pope a boxed set of writings by the black civil rights leader Martin Luther King.

The Pope gave Mr Trump a signed copy of a message he delivered for World Peace Day, along with some of his writings about the need to protect the environment. “Well, I’ll be reading them,” Mr Trump told him.

Seeking common ground – analysis by the BBC’s Jon Sopel

It is hard to think of two more contrasting characters than Pope Francis and President Trump.

On one hand, the Jesuit who has made his mission the championing of the poor and dispossessed; on the other the property developer who has championed getting rich, and surrounded himself with billionaires in his cabinet.

And though this is their first meeting, they’ve already sparred. During the election the Pope on a visit to the Mexico-US border said that people who only think of building walls instead of bridges were not Christian.

Donald Trump described those comments as disgraceful, and accused the pontiff of being a pawn of the Mexican government.

But on Wednesday both men were seeking to find common ground.

After his visit to Saudi Arabia, home to Islam’s holiest sites, and to Israel, this is the final leg of the tour of three of the world’s major religions.

President Trump’s commitment to fighting extremism and intolerance will win approval from the Pope, as will his determination to bring peace to the Middle East.

And the president thinks there’s another reason why they will get on. Back in 2013 he tweeted: “The new Pope is a humble man, very much like me.”

And the entourage?

Mr Trump was joined not only by his wife, daughter and son-in-law but also Secretary of State Rex Tillerson and National Security Adviser HR McMaster.

Both Melania and Ivanka Trump were dressed in black with their heads partially covered, in keeping with a traditional Vatican protocol that is no longer expected to be rigorously observed.

Melania, a Catholic, asked the Pope to bless her rosary beads. In a light-hearted exchange, Pope Francis asked her what she gave her husband to eat, suggesting “pizza”. “Yes, pizza,” she replied.

What next for Mr Trump’s trip?

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.

Read more from Katya

Mr Trump will end his tour on the Italian island of Sicily at the G7 summit on Friday.