Israel has yet to say what needs to be done before the talks can be restarted, the Palestinian leader told reporters Saturday.
"We were told it would happen soon," Abbas said, adding "by early July something should happen on this front."
Abbas was Cairo to meet with Egyptian President Hosni Mubarak after meeting with U.S. President Barack Obama in Washington, Ynetnews.com reported.
After meeting with Abbas, Obama said he was confident Israel would see a two-state solution as the best result for both sides.
A spokesman for the Palestinian extremist group Hamas said he heard nothing new from the meetings in Washington and Cairo that would result in peace between Israelis and Palestinians, Ynetnews.com said.
Israel still wants to turn the "Palestinian Authority into an armed wing of Israel that will eventually annihilate the resistance groups and perpetuate the internal Palestinian rift," Hamas spokesman Fawzi Barhoum said.