Peace talks sponsored by Washington hit a new impasse at the end of March when Israel refused to release a final batch of Palestinian prisoners and the Palestinians retaliated by seeking membership of several international treaties.
US Secretary of State John Kerry, who fought hard to kick-start the talks last July, this week blamed Israel for the latest deadlock as Washington mulled how much more time and effort to put into the faltering negotiations.
Also present were Yitzhak Molcho, a confidant of Prime Minister Benjamin Netanyahu, and Palestinian intelligence chief Majed Farah, the source said, speaking on condition of anonymity.
The Palestinians were pushing for the release of a final batch of prisoners, a commitment Israel reneged on at the end of last month in a move which sparked the crisis.
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Israeli public radio confirmed today's meeting was taking place but gave no details.
Israeli television later reported that the two sides were on the verge of a deal to extend peace talks beyond their original April 29 deadline.
The deal, which could be finalised within "a few days", would see a final batch of Palestinian prisoners released in return for Washington freeing American-born Israeli spy Jonathan Pollard, Channel 2 television said.
In Washington, however, a US official, asking not to be named, told AFP that the "reports are incorrect", without going into details.
The Israelis have repeatedly asked Barack Obama and previous US presidents to release Pollard, who is serving his sentence in North Carolina for passing US secrets on Arab and Pakistani weapons to Israel during the mid-1980s.