Obama presented Francis with a metal sculpture of an ascending dove, known as an international symbol of peace. The dove is also the Christian symbol for the Holy Spirit, one of the three aspects in the Trinity.
The personalized sculpture was made from an original armature bar from the Statue of Liberty, which was preserved during the centennial restoration of Lady Liberty in 1986, and the sculpture's pedestal was made from wood from the White House lawn, according to a White House official.
Obama also gave the pope a key from Elizabeth Ann Seton's home in Maryland dating back to the early 1800s. Seton, who dedicated herself to serving the poor, sick and vulnerable, was the first native-born American to be declared a saint.
The pope was welcomed by Obama to the White House, where Francis praised the president's efforts to battle climate change.
The pontiff then headed to the Cathedral of St. Matthew the Apostle after the Papal Parade, where he spoke out against sexual abuse committed by Catholic Church officials.
On Thursday, the pope will address a joint meeting of Congress at 9:20 a.m. before visiting the St. Patrick Catholic Church and Catholic Charities of the Archdiocese of Washington starting about 11 a.m.
After visiting Washington D.C., the pope will head to New York City and Philadelphia.