PA security forces have stopped more than 10 terrorist attacks against Israel since January, a second Palestinian source told Israel Radio.
U.S. Secretary of State John Kerry is expected to return to the region next week in an attempt to restart the talks, Israeli officials say.
Kerry's visit had been expected this week but was postponed after his wife fell ill.
The trip would be the secretary of state's sixth visit to the Middle East. The State Department had little confidence the result will be any different this time, U.S. sources have said.
As in previous initiatives, Kerry has counted on support from Arab states. However, two of those states -- Egypt and Syria -- currently have no functioning governments. Two others, Jordan and Lebanon, are dealing with an overflow of refugees from the Syrian conflict.