Israel is believed to be nuclear armed, though it does not confirm it
Senior Israeli and Iranian officials have met face-to-face and discussed the threat of nuclear arms, Israel says.
Israeli officials told the BBC each side attended panel sessions of a disarmament and non-proliferation conference in Cairo in September.
Iran had denied the Israeli accounts, but if confirmed it would be the first official exchange between the bitter foes since Iran's 1979 revolution.
Israel is believed to have nuclear arms and accuses Iran of seeking them too.
Representing Israel at the closed-door event at the Four Seasons hotel in the Egyptian capital was the head of arms control at the Israeli Atomic Agency, Meirav Zafary-Odiz, Israeli media reported.
Jon Leyne, BBC Tehran correspondent
One expert on Iran once said the Islamic Republic rests on three pillars: "Death to America," "Death to Israel" and "Long live the Hijab" (the Islamic headscarf for women)
"Death to Israel" is the most firmly held tenet of the true believers. Almost any bad news for the Islamic Republic is routinely blamed on "Zionists".
At news conferences abroad, Iran's officials refuse to listen to questions from Israelis, let alone answer them. Its international sports stars do their utmost to avoid competing alongside Israelis.
Iran has dealt with Israel when it has had to, mostly through third parties. In the Iran-Contra affair, it bought Israeli arms via the US.
Nevertheless, the possibility of direct negotiations between Iran and Israel on something as sensitive to both countries as the nuclear issue, appears extremely remote.
Iran's ambassador to the UN's nuclear watchdog, the IAEA, Ali Ashgar Soltanieh, was also reportedly at the conference.
Reacting to the reports, Iran's atomic energy organisation spokesmen denied any meetings had taken place with Israeli officials.
"This lie is a kind of psychological operation designed to affect the constant success of Iran's dynamic diplomacy in the Geneva and Vienna meetings," said Ali Shirzadian in quotes broadcast on Iranian state TV.
A senior Israeli government official, meanwhile, described it as "preposterous" that the Cairo panel sessions implied any kind of diplomatic contact between Iran and Israel.
"For years Iran and Israel have participated at the same time in multilateral forums like this," he said, giving the examples of UN agencies, and the IAEA.
Iran does not recognise Israel and the two sides are frequently involved in exchanging hostile threats and denunciations.
At international conferences and sporting events, representatives of the Islamic Republic invariably avoid any contact with their Israeli counterparts.
Israel's Haaretz newspaper says three panel sessions of the International Commission on Nuclear Non-Proliferation and Disarmament conference involved exchanges between the Iranian and Israeli delegates.
The sessions dealt with efforts to make the Middle East a nuclear-free zone, non-proliferation in the region and developing peaceful nuclear energy.
In one of the discussions, Haaretz quotes Mr Soltanieh directly asking Ms Zafary-Odiz: "Do you or do you not have nuclear weapons?"
Ms Zafary-Odiz reportedly smiled, but did not respond.
The newspaper says the two representatives did not meet separately outside the session or shake hands.
Israel is widely believed to have a stockpile of atomic warheads with delivery systems, but it refuses to confirm or deny their existence and has not signed the international Nuclear Non-Profileration Treaty.
The US leads accusations that Iran is engaged in a covert attempt to develop nuclear weapons, although Iran says its nuclear activities are purely for peaceful ends.