In it, Morsi appeared to write in English, "I am looking forward to exerting our best efforts to get the Middle east Peace Process back to its right track in order to achieve security and stability for all peoples of the region, including that Israeli people." The Israeli president's name was spelled "Perez."
Then a spokesman for Morsi, Yasser Ali, said in Cairo that Morsi had not written a letter to the Israeli president at all.
"This is totally untrue," Ali said, calling the letter a "fabrication." He blamed two Israeli newspapers for manufacturing the letter - though it was released by the president's office in Jerusalem.
An official in Peres' office - speaking anonymously because the issue concerned sensitive diplomatic relations - said the president's aides received the official communique Tuesday from the Egyptian ambassador to Israel, both by registered mail and by fax from the embassy in Tel Aviv.
Peres's office asked the Egyptian ambassador if it could publicize the letter or if it should be kept secret, the official said. The Egyptian envoy phoned Morsi's office to inquire, the official said, and then told Peres' aides that Morsi's staff had given the green light to make the letter public.
Peres's office sent reporters a copy of what was said to be the faxed letter. The top of the letter featured a time stamp with Tuesday's date, the phone number from which the fax was sent, and the label "EGY EMB TEL AVIV."
The fax number, which appeared to be printed automatically from the machine that sent the message, was a number listed on Israel's Foreign Ministry website as belonging to the Egyptian Embassy in Israel.
The Egyptian Foreign Ministry did not provide an immediate response on the issue.
This could be a symptom of Egypt's murky governing situation. Though Morsi has taken office, it is still not clear what his powers are.