"I urge all parties to avoid actions that risk undermining the negotiations," Ban told a news conference after a meeting with Israeli President Shimon Peres here.
"Both sides need to sustain an environment conducive for the peace process to move forward," he said two days after peace talks resumed here.
The UN Secretary General appealed to both sides to overcome "deep scepticism" and to be patient for peace to succeed. "We must overcome the deep scepticism that comes from 20 years of stalemate," he said.
The first round of direct Israeli-Palestinian talks on Wednesday lasted about five hours. Both sides imposed a media blackout though reports said negotiators would meet again weekly. Both sides remained cautious about breakthroughs.
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Hours ahead of the talks, Israel freed 26 of 104 Palestinian prisoners to be released to bolster the talks.
Ban said Israel has legitimate security concerns and should not have to live in perpetual fear. But he was hopeful the peace process would advance smoothly and said he and Peres were in agreement on direct negotiations.
In his discussions with Peres, Ban focused on how the UN and the world community can support progress towards a two- state solution that will ensure security for both Israelis and Palestinians.
Israel has much to contribute regionally and globally, said Ban, "But for that, we need peace." He said the UN will do everything possible to contribute towards that aim.
In welcoming Ban, Peres said he had come at the right time and for the right purpose, namely to support the beginning of peace negotiations.
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. "Had it been bad, it would have been leaked," he pointed out.