Charlie Flanagan is representing the Irish Government
Palestinian president Mahmoud Abbas and Israeli prime minister Benjamin Netanyahu shared a handshake and a brief exchange of words at the funeral of Shimon Peres.
The sombre ceremony for the former president and prime minister of Israel was attended by world leaders and dignitaries from 70 countries.
Foreign Affairs Minister Charlie Flanagan is representing the Irish Government.
Mr Abbas, who had taken part in peace negotiations with Mr Peres, was sat in the front row for the ceremony on Mount Herzl in Jerusalem.
The Palestinian president posted the meeting on Twitter:
US President Barack Obama, Britain's Prince Charles and former US president Bill Clinton were also at Israel's national cemetery.
In Mr Obama's eulogy to Mr Peres said Mr Abbas's presence was "a reminder of the unfinished business of peace".
"Shimon never saw his dream of peace fulfilled. And yet he did not stop dreaming, and he did not stop working," he added.
"It is that faith, that optimism, that belief, even when all the evidence is to the contrary, that tomorrow can be better, that makes us not just honour Shimon Peres, but love him. The last of the founding generation is now gone.
"Toda rabah haver yakar," he added - Hebrew for "Thank you so much dear friend".
The Nobel Peace laureate considered one of the founding fathers of Israel and his rich political career spanned seven decades.
Mr Netanyahu, who was a political rival to Peres, recalled a late-night discussion on Israel's future with Mr Peres discussing security and peace.
"Be at peace, Shimon, dear man, exceptional leader," he said.
"He was a great man of Israel. He was a great man of the world. Israel grieves for him. The world grieves for him," he said.
Friday's ceremony was Israel's largest gathering of international dignitaries since the funeral of Prime Minister Yitzhak Rabin, who was assassinated by a Jewish nationalist in 1995.
Mr Peres' children described the personal side of their father, with his daughter Tzvia Walden reflecting on his "forbearance and infinite patience".
She said: "He measured long and short on a timeline of two thousand years of history when weighing the state of the nation, but in nanoseconds when waiting for a text to be printed.
"He was ready with his new corrections even before the ink was dry. A day after lending me a book, he was astonished to learn that I had not yet finished reading it."
Born in Poland in 1923, Mr Peres emigrated to what was then British mandatory Palestine when he was 11.
He held nearly every major office in Israel - serving twice as prime minister (1984-1986 and 1995-1996) and also as president (2007-2014).
He died at the age of 93, two weeks after suffering a stroke.
Mr Peres' casket lay in state on Thursday outside the parliament building, where some 30,000 people filed past to pay their respects.