"Egypt is an important country in the region and what the region needs is synergy between Iran and Egypt, and we believe in taking new steps to improve our relations,” Iranian Foreign Ministry spokesman Nasser Kanaani said on Monday in his weekly press briefing.
There was no immediate comment from the Egyptian Foreign Ministry on Mr Kanaani's statement. However, both the ministry and the presidency welcomed Friday's announcement on the resumption of relations between Riyadh and Tehran, saying they hoped it would result in defusing regional tensions.
Tehran's relations with Cairo, a close ally of Saudi Arabia and other Gulf nations, have been fraught since the ousting of Iran's shah Mohammad Reza Pahlavi in the 1979 Islamic revolution. The shah's subsequent refuge in Egypt, then under the rule of president Anwar Sadat, worsened relations.
The shah died in 1980 in Egypt, where he is buried.
Relations deteriorated when Iran's clerical government named a Tehran street after Khaled Al Islambouli, who led a team of assassins that killed Mr Sadat during a 1981 military parade in Cairo. Repeated requests by Cairo to remove his name were denied.
More recently relations have been tense over what Cairo sees as the meddling of non-Arab and Shiite Iran in the internal affairs of Arab nations, such as Iraq, Syria, Lebanon and Yemen.
Unlike Saudi Arabia, which closed its embassy in Tehran in 2016, Egypt has maintained diplomatic representation in Tehran since the Islamic revolution. However, it has left only a charge d'affaires running its mission in the Iranian capital while Iran has a functioning embassy in Cairo led by an ambassadorial-level diplomat.
Egyptian officials familiar with Cairo's relations with Iran say the two countries have maintained sporadic contact over the years.
Like Saudi Arabia, Egypt is a regional heavyweight. While the kingdom is home to Islam's holiest shrines, Cairo's 1,000-year-old Al Azhar Mosque is considered the world's primary seat of Sunni Islam learning. Egypt is also the most populous Arab state with more than 100 million people.
Despite Friday's move, Saudi Foreign Minister Prince Faisal Bin Farhan sought to temper expectations of the diplomatic deal. In an interview published on Monday in the Saudi-owned Asharq Al Awsat daily, he said the agreement "does not mean that all pending issues between the two nations have been solved".