May 15 is celebrated as Independence Day by Israelis, the anniversary of the declaration of their state in 1948, but for Palestinians it marks the Nakba, or catastrophe.
A day before Nakba Day protests, Abbas said every Palestinian "has the right to see Palestine and return to the homeland because the homeland is our final destination," The Jerusalem Post reported.
Abbas promised his Palestinian Authority would pursue "practical steps" to achieving a right of return, but did not specify them.
"Of course, the other side does not want to discuss the issues of refugees, Jerusalem and water and that's their business," he said. "Does this mean that we should surrender to what they want? Of course not."
He also reiterated that the Palestinians would never accept a state without East Jerusalem as its capital.
Abbas said his Fatah movement and Hamas, which recently signed a unity deal, are working on establishing a non-party interim government.