Israeli and Palestinian negotiators said they aim to reach a definitive and comprehensive peace agreement within nine months, US Secretary of State John Kerry said.
Speaking at the end of a trilateral meeting with Israeli Justice Minister Tzipi Livni and Palestinian chief negotiator Saeb Erekat, Kerry said the "path is difficult" but "times are mature for a lasting peace".
"We had constructive and positive meeting," Kerry, flanked by Livni and Erekat, told a press conference at the US Department of State in Washington.
The secretary of state said both parties agreed to remain engaged in "sustained negotiations" and will meet again within the next two weeks in Israel or the Palestinian territories to begin formal discussions.
Kerry said all kinds of issues, whether core or minor, were on the table for negotiation but the discussions will remain confidential until a final agreement is reached.
He stressed the importance of compromises and praised both the Israeli and Palestinian leadership for the courageous choice that led to the reopening of negotiations.
On Sunday, Israel approved the release of more than 100 Palestinian prisoners as a goodwill gesture to mark the resumption of negotiations.
Kerry said the two-state solution was the only viable option, adding: "Each side has a stake in the other's successand everyone can benefit from the dividends of peace."
"We cannot pass along to another generation the responsibility of ending a conflict that is in our power to resolve in our time."
Livni and Erekat arrived in Washington earlier this week, to restart Middle East peace talks after five years of diplomatic stalemate.
The two were brought to the negotiating table by intensive brokering from US Secretary of Kerry, who has made six official visits to the Middle East in an effort to re-launch the peace process.
They both seemed to share Kerry's optimism about the peace process.
"Palestinians have suffered enough," said Erekat. "It is time for them to live in peace, freedom and dignity in their own independent state."
An emotional Livni thanked Kerry for showing them that "failure is not an option", adding that Israel was "hopeful but can't be naïve," as there will be difficulties to overcome.
"It is not our intention to argue about the past but to find solutions for the future," she said.
"I believe that history is not made by cynics but realists who are not afraid to dream, and let us be these people," she concluded.
Earlier President Barack Obama met the lead negotiators for the Israeli and Palestinian delegations privately at the White House.
Obama said the talks marked a "promising step forward," although "hard work and hard choices remain ahead."
Both Livni and Erekat thanked him for his mediation efforts.