A letter to Israel from Egypt's new president hoping for regional peace kicked up a stir on Tuesday when the Egyptian leader's Islamist movement denied that he had sent it. Israel insisted the letter was genuine.

The spat underlined the touchy nature of Egyptian-Israeli relations, always frosty but now especially sensitive in the wake of Muslim Brotherhood victories in the Egyptian elections. It also appeared to show some disarray in the fractured Egyptian government.

The letter, ostensibly sent by Egyptian president Mohammed Morsi, was a response to a message from the Israeli president, Shimon Peres, conveying Israel's good wishes for the Muslim holy month of Ramadan.

The return letter, released by the Israeli president's office, was on the stationery of the Egyptian embassy in Tel Aviv.

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's office – speaking anonymously because the issue concerned sensitive diplomatic relations between the two countries – said the president's aides received the official communique on 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 publicise 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's aides that Morsi's staff had given the green light for the letter to be made 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. The military council that took over after longtime president Hosni Mubarak was ousted last year assumed some presidential powers.

Also, the Brotherhood-dominated parliament has been dissolved, the military-appointed cabinet is still in office, and the ministries and foreign service are mostly still in the hands of the old regime. The disarray has led to conflicts, misunderstandings and power plays.

All that is in addition to the already complicated relations between Israel and Egypt. The two signed a peace treaty in 1979 but have rarely been close.

Morsi has pledged to respect Egypt's international treaties, but the Brotherhood has said it may need to make adjustments to the Israel-Egypt peace agreement. The movement has historically been hostile to Israel.

The Ramadan message was Peres's second letter to Morsi since he took office after winning Egypt's first ever free presidential election. The first, accompanied by a note from prime minister Benjamin Netanyahu, was sent in late June. It congratulated Morsi on his election victory and emphasised the importance of peace to both Israel and Egypt.

The text of Netanyahu's letter was not released, but an official in his office said the letter expressed his desire to maintain the peace treaty.