Israel's prime minister Benjamin Netanyahu has said is ready to sit down with Palestinian president Mahmoud Abbas for continuous one-on-one talks until they reach a peace deal.
Mr Netanyahu issued his statement on Sunday after a Palestinian man was killed in the West Bank after reportedly trying to attack Israeli troops at a checkpoint.
The offer of non-stop talks was an apparent bid to breathe life into the stalled Middle East peace-making.
Talks broke down in late September, just three weeks after they were launched at the White House, following the expiration of a limited Israeli freeze on settlement construction.
Mr Abbas says Israel must halt all settlement construction on occupied lands claimed by the Palestinians before talks can resume.
Mr Netanyahu has refused, but says he is ready to discuss all "core" issues with Abbas. Those include setting the final borders between Israel and a future Palestine, determining the fate of millions of Palestinian refugees and resolving the competing claims to the holy city of Jerusalem.
This weekend Mr Abbas said he believed a peace deal could be reached within two months if Mr Netanyahu showed "goodwill". He suggested that Mr Netanyahu adopt the positions of his more dovish predecessor, Ehud Olmert. "We were close to an agreement," said Mr Abbas. "The Palestinian position is clear to the Israelis and the Israeli position presented by Olmert is clear to us."
Mr Olmert has said he offered the Palestinians virtually all of the West Bank and parts of east Jerusalem - captured areas claimed by the Palestinians for their state - before negotiations broke down in late 2008.
Mr Netanyahu, who leads a more hardline coalition government, has given little indication that he is prepared to make similar concessions. But in response to Mr Abbas' comments, Mr Netanyahu said he "is ready to immediately sit down with Abu Mazen for continuous direct, one on one, negotiations until white smoke wafts" - an allusion to the Roman Catholic Church's method of signalling the choice of a new pope.
"If Abu Mazen agrees to my proposal that of directly discussing all the core issues, we will know very quickly if we can reach an agreement," he said.