Fayyad, on his part, said peace cannot be achieved unless the idea of a Palestinian state is accepted.
"While security, stability and peace should continue to be the driving force ... it is my judgement that unfortunately ... there can't be permanent peace unless the concept of Palestinian statehood, the concept of an sovereign, viable, independent state of Palestine is accepted."
Al Jazeera's Jacky Rowland, reporting from the conference, said the annual Herzliya meeting has gained a reputation as being used as a platform for new policies to be aired.
"[This is] basically because this was the forum that the former prime minister Ariel Sharon chose to announce his plans to pull settlers and troops out of Gaza, something that happened in August 2005.
"Since then, people have been paying a lot of attention to this conference in anticipation new policies could be mentioned."
Our correspondent said there had been some excitement in the audience ahead of the Fayyad-Barak session, but that the discussion was not expected to accelerate peace talks.
"[Fayyad] did get quite a warm welcome but ultimately I really [cannot] see this forum as being anything that is actually going to in any way accelerate the resumption of talks between Israelis and Palestinians."
The seminar was the first time senior Israeli and Palestinian officials have met since the peace talks broke down more than a year ago.
The Palestinians have said they will not return to the negotiation table until Israel halts its settlement activities in the West Bank.
The Israelis have on the other hand said they are ready to resume negotiations but accused the Palestinians of setting preconditions.