"We must overcome the deep scepticism that comes from 20 years of stalemate," Ban said at a meeting with Israeli President Shimon Peres here.
"I urge all parties to avoid actions that risk undermining the negotiations," a statement quoted the UN Secretary General as saying.
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"Both sides need to sustain an environment conducive for the peace process to move forward," he said, two days after peace talks resumed here.
Ban urged all the parties involved in the peace negotiations between Israel and the Palestinians to refrain from doing anything that would undermine the peace negotiations, The Jerusalem Post reported.
He made the request at a news conference in Jerusalem immediately following the working meeting with Peres.
Ban had made a similar request the previous day in Ramallah following his meeting with Palestinian Authority President Mahmoud Abbas.
This is his sixth visit to the region since taking office in 2007.
Israel has legitimate security concerns and should not have to live in perpetual fear, said Ban, who noted that his current visit was "at a crucially important time".
He was hopeful that the peace process would advance smoothly and said that he and Peres were in agreement on direct negotiations, and that both commended the efforts of the US, particularly those of Secretary of State John Kerry in facilitating the renewal of the peace talks.
Ban and Peres were also equally appreciative of the commitment of both Israel and the Palestinians along with that of the Arab initiative for regional stability.
In his discussions with Peres, Ban focused on how the UN and the international community can support progress to a two- state solution that will ensure security for both the Israelis and the Palestinians and will lead to greater prosperity for Palestinians in the West Bank and Gaza.
Israel has much to contribute regionally and internationally, said Ban, "But for that, we need peace." He stated that UN will do everything possible to contribute towards that aim.
In welcoming Ban, Peres told him that he had come at the right time and for the right purpose, namely to support the beginning of the peace negotiations.
The birth was not easy, said Peres, "but that the fact is that the talks are being conducted, not without difficulties, but with hope."
Despite the negative predictions, Peres said, the talks are taking place and things have happened.
He cited the preliminary meeting in Washington, the release of Palestinian prisoners, and the beginning of the peace talks which had started off not too badly, he said. "Had it been bad, it would have been leaked," he pointed out.