Mr Talabani (left) and Mr Barak spoke to one another
Iraqi President Jalal Talabani has shared an historic handshake with Israeli Defence Minister Ehud Barak.
The brief meeting took place at an international conference near the Greek capital, Athens.
Iraq does not recognise Israel and under Saddam Hussein was for years an implacable foe of the Jewish state.
The two men also held a short conversation, on the sidelines of the 23rd Socialist International Congress at Lagonissi coastal resort.
Mr Barak also held a private, half-hour meeting with Palestinian Authority President Mahmoud Abbas.
At the end of the meeting, the Israeli minister expressed hope that the two sides would reach a breakthrough in peace talks.
Mr Talabani's office downplayed the handshake with Mr Barak in a statement which described it as a "civilised social act" without special significance.
The statement said he was was responding to a request from Mr Abbas and was acting as leader of his Kurdish party and deputy president of the Socialist International, not as Iraq's president.
"It does not mean any obligations for the state of Iraq... and will not affect its support for the Palestinian people and the Palestinian Authority and reliance on Arab unity, the Arab initiative and legitimate international resolutions," the statement said.
Despite its close ties to Israel's main ally the US, the Iraqi government does not have diplomatic relations with Israel, putting it in the same category as all Arab states except Egypt and Jordan.
Addressing the conference earlier, Mr Abbas said Israeli-Palestinian talks "still face great obstacles".
"There is still a wide gap between the respective positions that cannot be overcome unless the Israeli government adopts positions and measures that will clearly emphasize its sheer desire to seize an opportunity to achieve peace," he said.
More than 600 participants from 150 political parties across 120 countries are attending the three-day conference.
Under the theme of "global solidarity", the meeting is covering climate change, peace and the resolution of conflict, the world economy and migration issues.
Mr Barak is attending the conference in his capacity as chairman of Israel's Labour party.
Mr Talabani was a founding member of the Patriotic Union of Kurdistan (PUK), one of Iraq's largest Kurdish parties.