Iranian President Mohammad Khatami has denied speaking to Israel's president at the funeral of Pope John Paul II.
The Mid-East leaders were sat just seats apart
Moshe Katsav says they exchanged words, but Mr Khatami told Iranian media the "allegations are false" and that they had not shaken hands.
Syria has confirmed that its leader shook hands with the Israeli president, but added that this did not change Syria's position on the Jewish state.
Iran and Syria do not recognise Israel. Syria and Israel are officially at war.
Mr Katsav, who was born in Iran, said he had exchanged words in his native Persian with Mr Khatami.
"These allegations are false... I have not had any meeting with a personality from the Zionist regime," the official Iranian news agency quoted Mr Khatami as saying.
Tens of thousands of people, including 200 world leaders, attended the burial of Pope John Paul II in St Peter's Basilica at the Vatican in Rome.
Mr Katsav first shook hands with Syria's Bashar al-Assad - who was seated a row behind him - as the funeral ceremonies began.
Mr Assad later initiated a second handshake as the funeral ended, but Syrian media said it did not indicate any change in relations.
"The protocol required that participants shook hands as a formality ... it had no political significance and does not represent a change in Syria's position," Syria's official news agency said.
Mr Katsav told the website of the Israeli newspaper Maariv that the first handshake occurred when he turned to shake hands with the nearby Swiss president.
"The Syrian president also stood there. We exchanged smiles and shook hands," Mr Katsav said.
"During the prayers, according to the Christian tradition, we exchanged handshakes... During this, it was the Syrian president who extended his hand to me and we again shook hands," Mr Katsav said.
Mr Katsav said that as he was leaving, "the Iranian president held his hand out to me. I shook his hand and greeted him in Farsi [Persian]."
The two men are reported to have talked about Yazd, the city in central Iran where both were born.
According to reports, Mr Katsav also embraced Algerian President Abdelaziz Bouteflika. Algeria and Israel do not have diplomatic relations.
Mr Katsav's spokeswoman, Hagit Cohen, called the exchanges historic, but said it was too early to say whether the handshakes would lead to any diplomatic breakthroughs.
"There is no doubt that this is a precedent, it was a historic moment and unique opportunity," Mrs Cohen said.
But Mr Katsav himself played down the significance of the encounter.
"When heads of state meet, they always shake hands," he told Israel's Yediot Ahronot newspaper's online edition.
"I don't think we can really say the ice has been broken. We shouldn't attach too much importance to such politenesses."
Dignitaries were seated in alphabetical order, according to their countries. Mr Assad was seated in the row behind Mr Katsav. Mr Khatami was seated three seats to the left of the Israeli president.