Biden, the highest-ranking American official to visit Israel and the West Bank since President Barack Obama took office last year, was expected to throw his weight behind the US-brokered indirect talks.
Palestinian officials announced on Sunday that they were ready to take part in the talks, despite deep scepticism about the prospects for success.
Talks between the two sides 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.
Biden said it was crucial that both sides enter negotiations with a positive attitude. Scepticism mounts ahead of indirect Mideast talks
"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," he said in an interview with the Israeli daily Yediot Aharonot.
"If the talks develop, we believe that we'll be able to bridge the gaps and that the conflict will be ended," he said in the interview published in Hebrew.
Israel's hawkish Prime Minister Benjamin Netanyahu stressed that any peace agreement must take Israel's security into account.
"We are trying to advance -- and I believe we shall succeed in advancing -- the peace process, but this process is not a game, it's a real thing," he said in a statement.
"It concerns first and foremost security, and our security is not a piece of paper. In real agreements we must prevent missiles, rockets and terror," he said after talks with US Middle East envoy George Mitchell, who is also in the region.
"These are things on which I intend to vigorously insist in order to achieve an agreement which will last for generations."
Israeli media reported that Biden's mission was also to convince Israel not to attack Iranian nuclear facilities and give US-led efforts to impose sanctions on Tehran a chance.
Israel has called for crippling sanctions on Iran's energy sector to persuade it to halt its uranium enrichment programme, which Israel and the West suspect is aimed at developing a weapons capability.
Tehran has insisted the programme is purely for civilian purposes.
Israel, the region's sole if undeclared nuclear power, views Iran as its greatest threat after repeated predictions by President Mahmoud Ahmadinejad of the Jewish state's demise.
Biden refused to comment on the possibility of military action against Iran, but expressed Washington's 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 for Iran," Biden told Yediot Aharonot.
"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," he said.
Source: AFP Global Edition