The meeting held at Mubarak's private residence in the Cairo suburb of Heliopolis lasted 30 minutes on Friday, after which neither leader made any comment to reporters.
Quraya had been due to leave Egypt late on Thursday, but delayed his departure for the meeting with Mubarak, said Palestinian sources.
There was no official explanation as to why the Mubarak-Quraya talks on Egypt's security role in a planned Israeli unilateral withdrawal from the occupied Gaza Strip were cancelled.
But rumours gripped Cairo over the declining health of
76-year-old Mubarak, who has been at the helm for 23 years since the assassination of his predecessor Anwar Sadat.