That sign was fleeting, however.
In a day of diplomatic confusion that involved not only Egypt and Israel but also the visiting American defense secretary, Leon E. Panetta, Egyptian and Israeli officials contradicted each other’s accounts of how or even whether the two presidents had communicated, leaving the state of relations roughly where they began — in uncomfortable uncertainty.
The office of President Shimon Peres of Israel first raised expectations on Tuesday when it released a letter that it said it had received by fax from Mr. Morsi via the Egyptian Embassy in Tel Aviv. The letter thanked Mr. Peres for his earlier letter of congratulations at the start of the holy Muslim month of Ramadan and expressed hopes for more cooperation with Israel on peace and security issues.
Later in the day, however, an official spokesman for Mr. Morsi denied in a statement to an Egyptian newspaper that Mr. Morsi had sent any conciliatory messages, and called reports of such a letter “slander.”
The episode underscored the delicacy of ties between the neighbors, which have maintained a peaceful if publicly frosty relationship for three decades but face new tensions as Egypt comes more under the sway of Mr. Morsi and the Muslim Brotherhood. The Brotherhood, once repressed in Egypt, has long been hostile toward Israel, although its leaders have moderated their views in recent months. Among the Egyptian populace, antipathy toward Israel and support for the Palestinians run deep.
The dispute erupted as Mr. Panetta, visiting both Egypt and Israel, said Mr. Morsi was “his own man,” a sign of American support for a former leader of the Brotherhood.
But the denial, which came after Mr. Panetta left Cairo for Jerusalem, raised the possibility that Mr. Morsi and his aides were saying different things to different audiences, or that they were unprepared for the scrutiny that accompanies any public statements he makes on a matter as charged as Egypt’s ties with Israel. It was also possible that, as a spokesman claimed, the letter was a fake.
Mr. Morsi’s office has not explained what happened in any detail. But his official spokesman, Yasser Ali, told Al Ahram, the semiofficial state newspaper, that Israeli accounts of the exchange were fabricated.
“This is completely unfounded, and President Morsi did not send any letters to the Israeli president,” he was quoted as saying. “What the Israeli newspapers published in this regard on Tuesday is slander, and the slander will not stop.”
Later, Ahmed Abdel Atty, a top Morsi aide, responded, “Not true,” in a text message when asked if Mr. Morsi had sent the letter.
Mr. Peres’s office said the letter arrived through official channels, with the Israeli president’s military secretary serving as a conduit.
In a scanned copy of the fax, Mr. Morsi conveyed his “deep thanks” to Mr. Peres for his Ramadan greetings. He added, “I take this opportunity to reiterate that 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 letter bore Mr. Morsi’s typewritten name at the bottom, but it was not signed by hand. Looking as if it may have been dictated, it came on a plain piece of paper, with no letterhead or insignia of the Egyptian presidency. A cover note from the Egyptian Embassy bore official embassy letterhead.
News of the letter was received with surprise and enthusiasm by some Israeli officials and analysts, and with a degree of sobriety by others reluctant to draw too many conclusions about the future course that Egypt may chart.
Amid the concerns raised here by Mr. Morsi’s affiliation with the Muslim Brotherhood, an organization long considered virulently anti-Israeli, some experts saw the Egyptian president’s gesture as a promising sign that the decades-old peaceful relationship between Israel and Egypt, a cornerstone of regional stability, might remain on track.
“This gives us hope that things might work out after all with the Islamists,” said Efraim Inbar, director of the Begin-Sadat Center for Strategic Studies at Bar-Ilan University. Mr. Inbar said that he had been “expecting the cold peace to become cooler,” but that the letter signaled to the Egyptian bureaucracy a need for continuity.
Analysts noted the significance of Mr. Morsi’s mention of the peace process, viewing it as an indication that he wants Egypt to continue to play a central role.
Still, there were those who sought to play the letter down.
Isabel Kershner reported from Jerusalem, and Elisabeth Bumiller from Cairo. Mayy El Sheikh and Kareem Fahim contributed reporting from Cairo.