Trump's visit to Israel and the Palestinian territories is part of his first trip overseas as president, and follows an initial leg in Saudi Arabia, where he urged Islamic leaders to confront extremism.
"Our fundamental problem is with the occupation and settlements and the failure of Israel to recognize the state of Palestine", Abbas said. Ivanka Trump converted to Judaism to marry Kushner, an orthodox Jew.
Mr Trump approached alone and placed his hand on the stone.
If President Donald Trump concludes his first global trip by saying he made history "even while sitting on a plane", no one can say he's wrong. The U.S. has never recognized Israeli sovereignty over parts of the Old City seized in the 1967 war.
The visit raised questions about whether the USA would indicate the site is Israeli territory. Various officials have said that was the source of the classified intelligence.
It later annexed east Jerusalem and claims the entire city as its capital.
Previous U.S. presidents have declined to move the U.S. Embassy to Jerusalem as it would provide a powerful symbolic rejection of Palestinian - and Arab - aspirations for their own capital inside a separate state.
Trump promised to move the U.S. Embassy from Tel Aviv to Jerusalem while campaigning for president past year.
Trump was accompanied by the Western Wall's rabbi, Shmuel Rabinovitz, during his visit. Turning to the prime minister, who joined him for the speech, Trump said, "Benjamin Netanyahu wants peace". An Israeli TV station quoted an American as telling the Israelis that the wall is not in Israeli territory, enraging Trump's Israeli hosts.
But hours later, Nikki Haley, Trump's United Nations ambassador, asserted that the wall is part of Israel. We all know that.
Before visiting the Western Wall, Trump toured the nearby Church of the Holy Sepulcher, built at the site where Christians believe Jesus was crucified, buried and resurrected. Trump's perceived Saudi willingness to be part of a coalition to fight radical Islam were coupled, in his remarks in Bethlehem, with the notion that an Israel-Palestinian deal would ignite that cooperation, help crush ISIS and forge stability in the region.
It is widely assumed that Israel would retain control over the site under a potential peace deal.
The Wall sits at the base of a plateau which Jews call the Temple Mount and Muslims call the Noble Sanctuary. The traditional site of Christ's tomb, known as the Holy Edicule, recently underwent a yearlong renovation.
The competing claims sometimes spill over into violence, and the USA has withheld recognition of Israeli control of the area until there is a deal.
According to the White House, the visit affirmed the theme of Trump's first overseas trip, promoting unity and peace among the three Abrahamic faiths.
Trump landed at Ben-Gurion International Airport for a two-day visit to Israel and the Palestinian territories as part of his first trip overseas since taking office. No explanation was given for the dateline.
After a short meeting, Abbas and Trump held a press conference at the Presidential headquarters in Bethlehem.
To get to Bethlehem from Jerusalem, Trump's motorcade passed through streets lined with heavily armed security forces and an opening in Israel's towering separation barrier, a visual reminder of the complexities of the conflict in the region.