"We have got to ensure now that we will give the talks every chance of succeeding. The key is holding talks with goodwill, so that both sides come to the table with serious intentions," the US vice-president said.
"If the talks develop, we believe that we'll be able to bridge the gaps and that the conflict will be ended."
Talks between Israel and the Palestinians have been on hold since Israel launched a devastating offensive against the Gaza Strip in December 2008, despite US efforts to relaunch the peace process.
"Iran obtaining nuclear arms will deeply undermine the stability of the entire international community and could lead to a nuclear arms race in the Middle East"
Palestinian officials announced on Sunday that they were ready to take part in the talks, despite deep scepticism about the prospects for success.
Also in his interview with Yedioth Ahronoth, Biden emphasised Washington's efforts to drum up greater international pressure on Iran and said that Washington would close ranks with its ally Israel against any threat from a nuclear-armed Iran.
Asked about the prospect of an Israeli attack, he said: "Though I cannot answer the hypothetical questions you raised about Iran, I can promise the Israeli people that we will confront, as allies, any security challenge it will face.
"A nuclear-armed Iran would constitute a threat not only to Israel - it would also constitute a threat to the United States."
'Nuclear arms race'
Israel and the West have called for sanctions on Iran over its uranium enrichment programme, which Israel and the West say is aimed at developing nuclear weapons.
Iran has insisted its programme is for purely civilian purposes.
Biden refused to comment on the possibility of military action against Iran, but expressed US commitment to stopping Tehran from acquiring the bomb.
"Iran obtaining nuclear arms will deeply undermine the stability of the entire international community and could lead to a nuclear arms race in the Middle East that will be extremely dangerous for everyone involved, including Iran," he told the paper.
"For this reason, our administration is mobilising the international community to insist that Iran fulfil its international commitments. If it does not, it will have to deal with serious consequences and with increasing isolation."
During his trip, Biden is due to meet Shimon Peres, the Israeli president; Binyamin Netanyahu, the Israeli prime minister; and Tzipi Livni, the leader of Kadima on Tuesday.
On Wednesday, he is to hold talks with Tony Blair, the special envoy for the Quartet of diplomatic players in the peace process; as well as Mahmoud Abbas, the Palestinian president; and Salam Fayyad, the Palestinian prime minister.