The newly-elected Egyptian president has vowed to maintain the peace treaty with Israel signed more than 30 years ago.
Supporters of the Muslim Brotherhood were celebrating this weekend after the Islamist party's candidate, Mohammed Morsi, was declared the victor in the runoff election.
The once-banned party has said that it would protect the treaty but also suggested that it would call for modifications to it.
President Mohammed Morsi said he would "preserve international accords and obligations" after the result was announced.
Israeli officials offered cautious congratulations to the new president. "Israel appreciates the democratic process in Egypt and respects its outcome", said a spokesman.
"Israel expects to continue co-operation with the Egyptian government on the basis of the peace agreement between the two countries," said Israeli Prime Minister Benjamin Netanyahu. "It is of interest to the two peoples and contributes to regional stability."
The peace treaty was signed in 1979 and its existence is considered a cornerstone of Israel's security policy.
Britain's Foreign Secretary, William Hague, said he wished Mr Morsi success, but called for the new government "to stand for national unity and reconciliation, to build bridges across Egyptian society and to uphold human rights, including the rights of women and religious minorities, and the rule of law".
In Gaza, which is bordered by Egypt, the Brotherhood's success was also a cause for celebration, although reports said one person was killed by celebratory gunfire.
Hamas leader Ismail Haniyeh called the election result "a victory for all Arabs and Muslims".
"This is God's promise to his believers," he said.