US President Donald Trump has held his first meeting with Pope Francis at the Vatican.

The pair put their previous clashes behind them to display a show of peace in the brief talks.

Last year the pope criticised Trump's campaign pledges to build a wall on the Mexican border and turn away Muslim immigrants and refugees from the US.

"A person who thinks only about building walls, wherever they may be, and not building bridges, is not Christian," Francis said at the time.

The pontiff frequently calls for greater compassion for refugees and deemed it both a "moral imperative" and "Christian duty" to help.

Trump responded by calling Francis "disgraceful" for doubting his faith.

However, the pair met with a handshake on Wednesday morning ahead of a private 30-minute meeting.

Trump, 70, then introduced the 80-year-old pontiff to his wife Melania and his daughter Ivanka, who both covered their heads in a sign of papal respect, a gesture they did not partake in Saudi Arabia.

The president's delegation also included Ivanka's husband Jared Kishner, a top White house aide and National security adviser H.R. McMaster.

The meeting ended with a gift exchange and a lighthearted moment between the pope and the first lady.

Francis gave the president a medal featuring an olive branch, a symbol of peace, among other gifts.

"We can use peace," the president responded.

Trump presented the pontiff with a custom-bound, first-edition set of Martin Luther King Jr.'s works, an engraved stone from the King memorial in Washington and a bronze sculpture of a flowering lotus titled Rising Above.

"I think you'll enjoy them. I hope you do," Trump said.

A smiling Francis then asked Melania, via a translator, "What do you give him to eat, potizza?" referring to a favourite papal dessert from her native Slovenia.

"Yes," she confirmed.

The Vatican said it hopes for "serene collaboration" with the United States after the meeting.

The US President is halfway through a nine-day, maiden international tour.

Where the pope and the president agree:

The men have potential to disagree on: