Mohamed Morsi's victory in Egypt's presidential election has brought him congratulations from across the Middle East. But there have also been mixed feelings, loaded messages from Israel to Iran, and uncertainty about the future direction of policy.

Islamists everywhere were delighted by the historic achievement for Morsi's Muslim Brotherhood, but conservative monarchies hoping to avoid the Arab spring unrest were not. Compliments from Saudi Arabia, where King Abdullah still laments the overthrow of Hosni Mubarak, sounded distinctly formal.

Morsi's main challenges lie in the domestic arena, with the Supreme Council of the Armed Forces (Scaf) determined to hold on to its powers to control defence, foreign policy and internal security. "There will be no dramatic changes," predicted the Egyptian analyst Said Shehata.

Still, even a weak president will want to speak out on the sensitive issue of Egypt's peace treaty with Israel. The Brotherhood's position, reiterated on Sunday, is respect for international commitments, though that does not preclude an attempt to renegotiate military deployments in Sinai.

Abrogation of the 1979 treaty would return Egypt to a state of war that cost it thousands of lives and would risk strategic relations with the US.

It is hard, too, to imagine any tolerance for Mubarak-era support for the blockade of the Gaza Strip, where jubilant Hamas leaders hailed Morsi's victory as "a defeat for the programme of normalisation and security co-operation with the enemy". The Rafah border is likely to be more open to Palestinians, though without triggering an immediate crisis with Israel.

Yediot Aharonot, Israel's largest-circulation newspaper, expressed alarm about what it called "darkness in Egypt" – a reference to one of the biblical 10 plagues. That was in contrast to a terse formal message from Binyamin Netanyahu but reflected popular Israeli fears about the long-term dangers of the Arab spring.

Morsi's first foreign problem arrived from Iran, where a news agency quoted the new Egyptian president on Monday as saying he wanted to reconsider peace with Israel. That was swiftly and emphatically denied, as was the reported statement that he wanted to see a "balance of pressure" in the region.

US diplomacy towards Egypt is based on the assumption Scaf will retain control of these issues. The US will be anxious to keep overflight agreements and free passage through the Suez canal. The generals will not want to jeopardise $1.3bn in annual US military aid.

"Morsi will not make any difference on the Palestinians or the treaty with Israel," said Nadim Shehadi of Chatham House. "It will be a continuation of the old system when the military and Brotherhood play good cop/bad cop and keep the balance."

Middle East expert Juan Cole wrote in Informed Comment: "Mursi and his colleagues will only change things at the margins for US policy."

Morsi's reputation for caution was reinforced recently when he dismissed as "delusional, slanderous and baseless" the suggestion that the Brotherhood had direct relations with Iran or Hezbollah, its Lebanese ally. "We will never stand with the forces who threaten friendly countries in the Arabian Gulf," he pledged.

Iran and Saudi Arabia are at odds over Bahrain and Syria so any rapprochement between Cairo and Tehran would anger the Saudis and Gulf partners. That could risk economic aid and investment in Egypt.

The Saudis backed Ahmed Shafiq, Mubarak's last prime minister and Morsi's rival for the presidency. So whatever else happens, "Egypt's relations with Saudi Arabia will never be the same again," suggested Ahmed Asfahani, the respected al-Hayat columnist.

Jordan, another western-backed Arab monarchy nervous about the pressures of the Arab spring, will be privately unhappy about Morsi's victory – not least because it will encourage the country's Islamic Action Front, the political wing of the Muslim Brotherhood. Morocco shares similar concerns.

In Syria, where the Brotherhood makes up a significant part of the anti-Assad opposition, the government offered its formal congratulations, avoiding the awkward question of whether Damascus is likely to see a free and democratic election soon.