Rapprochement between Tehran and Cairo would worry the Arab world, unnerve Israel and dismay the United States.
Egypt's new government ready to renew country's ties with Iran
It is a street that symbolises three decades of animosity between two of the Middle East's oldest, proudest and most powerful rival civilisations.
Khaled Islambouli Avenue in a leafy, upmarket area of central Tehran was named in honour of an Egyptian army officer turned jihadi militant. Islambouli assassinated the Egyptian president Anwar Sadat in 1981, three years after Sadat signed the Arab world's first peace treaty with Israel.
Now Egypt's transitional new government says it is ready to re-establish diplomatic ties with Iran. If an agreement is clinched, the diplomatic repercussions will reverberate across the Middle East and beyond.
An historic rapprochement between Tehran and Cairo would concern the Arab world, unnerve Israel and dismay the United States, which has been striving to isolate Iran because of its nuclear programme.
Iran would hail a breakthrough with Egypt as the first concrete gain it has reaped from the pro-democracy unrest gripping much of the Arab world. The changing regional tide, Iran already argues, is in its favour.
Farideh Farhi, an Iran expert at the University of Hawaii, said: "Re-establishment of ties with Egypt would be very significant for Iran, particularly in the light of deteriorating relations with Saudi Arabia and other Gulf states. Iran has been trying to re-establish relations with Cairo for several years in order to counter its attempted isolation by the US."
Within a year of Iran's 1979 Islamic revolution, the new regime in Tehran severed ties with Egypt in protest at Egypt's 1978 Camp David peace treaty with the "Zionist entity".
Tehran was also furious that Egypt had given asylum to Iran's ousted dictator, Shah Mohammad Reza Pahlavi, who died of cancer in 1980 and was buried in Cairo.
But Egypt's new foreign minister, Nabil Elaraby, signalling a potentially dramatic shift in Iran policy after the removal of the Egyptian president Hosni Mubarak, said: "The Egyptian and Iranian people deserve to have mutual relations reflecting their history and civilisation."
Mr Mubarak was viscerally mistrustful of Iran, where he was derided as "an American puppet" and a calcified "pharaoh". He saw Iran as "the greatest strategic threat to the Middle East", according to a US diplomatic cable released by WikiLeaks.
But Mr Elaraby insists that Egypt does not consider Tehran an enemy, and says Cairo is "opening a new page with all countries, including Iran".
Stoking Israel's concerns, Mr Elaraby added that Hizbollah was part of Lebanon's political and social fabric, and that Egypt welcomed contacts with the Iranian-backed Lebanese organisation.
Mr Elaraby's outreach was hailed by his Iranian counterpart, Ali Akbar Salehi. Congratulating the Egyptian people on their "victorious" revolution, he said: "A good relationship between our countries will definitely help stability, security and development in the region."
The new Egypt, it seems, has taken a leaf from Turkey's foreign policy model: fostering good relations with neighbours and reaching out to both East and West.
Iran will, however, remain deeply suspicious of Egyptian motives.
"One of the reasons the Egyptians [are proffering an olive branch] is to use relations with Iran to improve their position regarding both Israel and the US," said Meir Javedanfar, an Iranian-born analyst in Israel.
He believes that ties between Tehran and Cairo will improve. "But it's unlikely in the long run that this will turn into a strong strategic alliance because they will not be able to overcome the age-old divide between Sunni Arabs versus Persian Shiites," he said.
Other experts have also to be convinced that Cairo is ready for a "fully normalised relationship" with Tehran.
Egypt's interim military government could well be using its flirtation with Iran as a bargaining chip to send a message to the US "that it needs to ease pressure on human rights issues and continue financial support", Ms Farhi said.
Mr Elaraby, who was appointed foreign minister on March 6, has been raising Israeli hackles on other fronts. Last weekend he insisted that Israel should no longer expect to receive exports of Egyptian natural gas at preferential rates. For good measure, he said Israel had regarded Mr Mubarak as a "treasure", and the days when the Jewish state could do as it pleases are over.
Cairo, Mr Elaraby insisted, would remain an important player in the Middle East peace process, but he complained: "The Palestinians want peace but Israel has not yet met their demands."
Tehran and Cairo appeared to be on the brink of renewing full diplomatic ties in 2004. Iran at the time had a reformist president, Mohammad Khatami, a popular, philosopher-politician who was determined to improve relations with the Arab world.
Khaled Islambouli Avenue was to be renamed Intifada Avenue, after the Palestinian uprising against Israel. It never happened.
A year later, in 2005, Mr Khatami was replaced as president by the firebrand hardliner Mahmoud Ahmadinejad. Ties with Egypt and the Gulf states soon deteriorated.
Ms Farhi believes Iran's hardline leadership now "will figure a way out to placate its base" on renaming the avenue for the "sake of improved ties" with a key Arab state.
Other experts are sceptical. One analyst in Tehran said: "Iran wants the new Egypt as a friend, but the government will bristle at changing the street's name. It would see agreeing to any such condition as sign of weakness."
Iranian hardliners would also have been angered by remarks on Sunday deemed insulting to Ayatollah Ruhollah Khomeini, the leader of Iran's 1979 Islamic revolution.
Seeking to reassure Egyptians that Islamists would not be allowed to come to power in elections scheduled for later this year, Egypt's Supreme Council of the Armed Forces proclaimed that "Egypt will not be governed by another Khomeini".