Pope Francis welcomed President Donald Trump to the Vatican on Wednesday, shaking his hand before ushering him into his study for the first face-to-face meeting of the two of the most powerful leaders who of the world.

The president’s motorcade rolled into the courtyard in an armored limousine. A few minutes before Mr. Trump’s visit, the pope arrived at the palace in a blue Ford Focus. He stepped out of the car and walked into a side entrance.

President Trump, who landed in Rome after stops in Saudi Arabia and Israel, the audience in the Vatican caps a tour of the ancestral homes of three of the world’s great monotheistic religions. For Francis, who recently made his own landmark visit to Egypt last month, it was a chance to welcome a second American leader, after President Barack Obama paid his respects in 2014.

Mr. Trump nodded with a serious face as Archbishop Gänswein made small talk. Behind them were Mrs. Trump, wearing a black dress and with her hair covered by a veil, and Ivanka Trump, the president’s daughter and adviser, also wearing a veil over her hair and in a black dress with lace hem and pearls.

They were accompanied by Jared Kushner; Secretary of State Rex W. Tillerson; and H. R. McMaster, the national security adviser, who paused to examine frescoes. With other members of the president’s retinue, they walked past seven Swiss Guards standing at attention in front of a white papal throne, halberds in hand.

The private audience ended at about 9 a.m., with the signaling of a bell, and soon after Mrs. Trump went into the pope’s studio.

The president smiled broadly as he stood next to Francis, who looked more serious but smiled as he shook Mrs. Trump’s hand. The president then introduced his daughter, Ivanka, and the rest of his delegation, beginning with Mr. Kushner.

The pope handed out rosaries to members of the delegation before the group posed for pictures, and then he bade the president and his wife farewell.