The president said the Palestinian leader "assures me he is ready to work toward" a peace deal.
No one had reported the president mentioned Israel at a meeting in which he is alleged to have shared highly classified information.
Making the first visit to the wall by a sitting American president, Trump came with his wife, Melania, daughter Ivanka and son-in-law Jared Kushner.
The group swore allegiance to the Spanish Constitution and the King thanks to a law passed two years ago.
The Jewish rapper's 13 honors, including as top artist, snapped the mark of 12 held by Adele.