WASHINGTON, Dec 10 (Reuters) - Secretary of State Hillary Clinton said on Friday the United States would push Israeli and Palestinian leaders solve the core issues standing in the way of peace, and that both must seek a deal despite a breakdown in U.S.-brokered direct negotiations.

Clinton, saying she shared frustration over the impasse in peace talks, said the United States would launch a new round of indirect shuttle negotiations aimed at making real progress in the next few months toward a framework peace deal.

The United States will not be a passive participant. We will push the parties to lay out their positions on the core issues without delay and with real specificity, Clinton said in an address

We will work to narrow the gaps, asking tough questions and expecting substantive answers, she said, adding that the United States would also offer its own proposals to move talks along when appropriate.

Clinton's speech marked her first Middle East policy address after the United States abandoned efforts this week to persuade Israel to stop new construction of Jewish settlements, a step the Palestinians said was essential if they were to resume direct peace talks which collapsed just weeks after their September launch.

The breakdown was a setback for President Barack Obama, who has made Middle East peace a key U.S. policy goal, and sowed tension between Washington and its most important Middle East ally as both face challenges including Iran.

U.S. Middle East peace envoy George Mitchell will head back to the region next week, and Clinton said diplomacy would now concentrate on a range of core issues -- all of which have proved difficult to resolve.

These include borders and security, settlements, water, refugees, and Jerusalem itself, which Israel says is its capital but which the Palestinians also hope will serve as the capital of their future independent state.

Their seriousness about achieving an agreement will be measured by their engagement on these core issues, Clinton said.

A CHANGE IN TACTIC?

U.S. officials have little to show for months of shuttling between Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas, both of whom are limited by domestic politics in how far they can go.

Daniel Levy, co-director of the Middle East Task Force at thee New America Foundation think tank, said Clinton's speech broke little substantive new ground but could signal a shift in U.S. tactics.

They are doing what might have been wise much earlier -- that is making indirect talks 'substantive 2-way conversations', Levy said. These are now the real thing.

Clinton paid special attention to the question of final borders, suggesting this could be a future U.S. focus.

They must agree to a single line drawn on a map that divides Israel from Palestine, and to an outcome that implements the two-state solution, she said. The Palestinian leaders must be able to show their people that the occupation will be over.

Clinton's speech followed a hectic week of personal diplomacy that saw her meet the chief Israeli and Palestinian peace negotiators, former Israeli foreign Minister Tzipi Livni as well as Palestinian Prime Minister Salam Fayyad and Israeli Defense Minister Ehud Barak, who both attended Friday's address at a Brookings Institution event in Washington.

Barak, in his own speech to the group, gave a strong endorsement to the peace effort, saying that only through allowing the Palestinians their own state could Israelis be secure in theirs.

Two states for two peoples is the only true path of Zionism today, he said.

Clinton repeated the rock-solid U.S. commitment to Israel's security, while underscoring yet again that the United States regarded as illegitimate continued Jewish settlement construction on Palestinian land occupied in the 1967 war.

The United States cannot impose a solution, she said, and Israelis and Palestinians themselves must take responsibility for peace and refrain from assigning blame.

There is no viable alternative to reaching mutual agreement. The stakes are too high, the pain too deep, and the issues too complex for any other approach, she said. (Writing by Andrew Quinn. Editing by Mohammad Zargham)