"If you have a chance to come to the White House, we can show you our garden as well," the president said.
"Como no," the pope responded, which translates to "why not?" or "for sure."
It was widely speculated that during their meeting the president might invite the pope to visit the United States.
The president's gift was inspired by the pope's decision to open to the public the gardens of the papal summer residence."These I think are carrots," Obama said, holding a pouch. "Each one has a different seed in it. The box is made from timber from the first cathedral to open in the United States in Baltimore."
The chest is made from American leather, and features reclaimed wood from the Basilica of the National Shrine of the Assumption of the Blessed Virgin Mary, one of the oldest Catholic cathedrals built in the United States. The Basilica's cornerstone was laid by John Carroll, a Jesuit and the first Catholic bishop and archbishop in the United States.
In return, the pope gave the president two medallions, which the president said he would "treasure" and a copy of Evangelii Gaudium or "The Joy of the Gospel," the 2013 apostolic exhortation by the pope which called for a renewed focus on the world's poor.
"I actually will probably read this in the Oval Office when I'm deeply frustrated. I'm sure it will give me strength and calm me down," the president said, smiling.
"I hope," the pope responded.
After the traditional exchange of gifts, the two walked together towards the door. "His Holiness is probably the only person in the world who has to put up with more protocol than me," the president joked.