It is not known when Martha and Pope first met.
The Pope also met privately with victims of sexual abuse by priests.
For 15 minutes, they waited together as the pope met privately with Israel's two chief rabbis.
The Pope meets Jewish groups on nearly all of his foreign trips.
But the Pope, unusually, did not meet with human rights leaders; indeed, he barely alluded to the horror.
The pope will meet with Muslim leaders, just as he did in Jerusalem last March.
It was only the third time since the Christian church divided in 1054 that a Pope and an Orthodox leader had met.
The pope had already met in January with Cardinal Law, who has been under pressure to resign over his handling of sexual abuse cases.
Mr. Bush and the pope met for 20 minutes in private with no aides and no translators.
The Pope was also in touch with Ağca's family over the years, meeting his mother in 1987 and his brother a decade later.