Mr Netanyahu said on Sunday that stalled peace talks between his government and the Palestinian Authority could resume in September.
Those parties generally support restarting long-stalled peace talks with the Palestinians.
With Abbas, Kerry was talking about ways to improve the Palestinians' living conditions as a confidence-building measure to improve the atmosphere for a resumption in stalled peace talks with Israel.
Besides pressuring the Sudanese government to rein in the janjaweed, Mr Annan has called on both the government and Darfur's rebels to stop violating their ceasefire and to press on with their stalled peace talks.
Syria contends that the late Israeli Prime Minister Yitzhak Rabin agreed during lower-level peace talks that stalled in 1996 to return the Golan, a water-rich region that overlooks the upper Jordan River valley.
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Others have taken the lead in trying to revive peace talks in Darfur, stalled since the total failure of a conference in Libya in October 2007.
Although the U.S. has finally found its footing on the reform issue, its aspirations of restarting Mideast peace talks between Israelis and Palestinians may be stalled indefinitely.
Talks on a peace deal which would give greater civil rights to Albanians stalled last week amid Macedonian criticism.
But today Israeli officials I have spoken to say they hope these new talks about the Arab initiative might help reinvigorate the long-stalled Arab-Israeli peace process.
Clinton and Hastert's telephone conversation took place as Israeli and Palestinian negotiators engaged in another day of long and difficult talks aimed at forging a lasting peace and permanent division of territory, with their arduous talks at Camp David reportedly stalled over the issue of the final status of the city of Jerusalem.
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