Diplomatic efforts to secure the release of Cpl. Gilad Shalit continued on two tracks Tuesday - both a Cairo and a Damascus track - even as Shalit's captors said the time for negotiations had ended. Egypt and Qatar were involved in Gaza in trying to hammer together a deal whereby the captors would release Shalit unharmed. The Qatari foreign minister has been in contact with Foreign Minister Tzipi Livni a couple of times over the last week to see what could be done to broker a solution. Hamas leader Khaled Mashaal, currently based in Damascus, went to Qatar in 1999 after being kicked out of Jordan. Russian and Turkish officials, meanwhile, were talking with Syria in an effort to press them to lean on Mashaal and ensure that Shalit is not harmed. Prime Minister Ehud Olmert hinted at this as well during a speech Tuesday at the Negev Economic Conference in Beersheba, saying that Israel would strike "those who sponsor" terrorism from the Gaza Strip. Livni spoke with Russian President Vladimir Putin in Moscow Sunday about the issue, and on Monday Turkish Prime Minister Recep Tayyip Erdogan sent his chief foreign policy adviser, Ahmet Davutoglu, to Damascus in what Turkish Foreign Minister Abdullah Gul said was a bid to convince Syrian President Bashar Assad to defuse the crisis. Olmert reiterated that Israel would not negotiate a "prisoner exchange" with Shalit's captors. "We won't negotiate with terror elements, and we won't let anyone believe that kidnapping is a tool to bring Israel to its knees," he said. "If we would do that today, we would be abandoning many Israeli citizens who tomorrow or the next day would be targeted if it becomes clear to somebody that kidnapping brings results." One diplomatic official said that while Israel has said it would not release Palestinian prisoners in order to release Shalit, it would "de-escalate" the current crisis and "re-deploy out of Gaza" if he were released. The London-based newspaper Al Hayat reported Monday that one deal being discussed was for Shalit to be sent to France or Egypt, and for rocket fire on Israeli cities to stop, in return for Israel's halting its military operations in Gaza and freeing the 64 Hamas activists arrested last week. Before attending the Beersheba conference, Olmert visited Kassam-wracked Sderot Tuesday, much like US President George W. Bush makes occasional visits to Baghdad - without any pre-visit publicity in order to stave off enemy fire. Olmert told participants at the Beersheba conference that he visited Sderot in this way because of the concern that terror groups would make every effort to fire at the town during his visit. This was Olmert's first visit to the town since becoming prime minister, and he said it was painful for him to go in that manner. Sderot Mayor Eli Moyal said that Olmert met with him and other regional leaders for only 15 minutes. He said he was told of the meeting only five minutes prior to Olmert's arrival. Vice Premier Shimon Peres, meanwhile, told Beersheba conference participants that Israel's deterrence had not been harmed by the Shalit affair. "I am afraid that our response to the crisis has been blown a little bit out of proportion," he said. "Our level of deterrence has not been harmed. Israel has a very high level of deterrence. This does not mean that we don't have problems, but this is a problem that does not endanger our deterrence." According to Peres, the Palestinians were the big losers in the crisis. "The Palestinians are jeopardizing their future. They will not be able to have a state in which soldiers are being kidnapped and Kassams are being fired."