According to media reports, the two sides discussed the Palestinian Authority's plan on the ground and at an international level to stop increasing Israeli violations at the al-Aqsa Mosque compound in East Jerusalem, Ma'an News Agency reported.
They also reportedly discussed other regional issues, with no further details provided.
Abbas arrived in the United States late Friday to attend the UN General Assembly.
Riyad Mansour, the Palestinian representative to the UN, told Ma'an that Abbas will meet with President Barack Obama and Secretary of State John Kerry to discuss his expected resignation as president.
Mansour added that Abbas would meet with a number of other international leaders between Sep. 26-30, when he will give his speech at the UN General Assembly.