Maikel Nabil says the Middle East has "had enough violence and confrontation."
Israel and Egypt signed a peace treaty in 1979, but relations have been cool, and visits like this are rare.
The 26-year-old blogger says he came to help mend ties strained further after the ouster of longtime Egyptian President Hosni Mubarak last year. Egypt's dominant Muslim Brotherhood is hostile to Israel.
Nabil said Sunday, "Being for Palestinians doesn't mean you have to be against the existence of Israel."
The trip has drawn criticism from fellow activists sympathetic to the Palestinians.
"If Israel would like to keep Maikel Nabil, there are no objections from me," tweeted Sarah Carr, another prominent Egyptian blogger.