In meetings with Israeli officials recently, Secretary of State Condoleezza Rice was forceful in expressing Washington's view on the matter.
The American argument is that even "exploratory talks" would be considered a prize in Damascus, whose policy and actions continue to undermine Lebanon's sovereignty and the functioning of its government, while it also continues to stir unrest in Iraq, to the detriment of the U.S. presence there.
It is also known that Syria, like Iran, continues to provide Hezbollah with arms and equipment.
According to senior Israeli officials, the American position vis-a-vis Syria, as it was expressed by the secretary of state, reflects a hardening of attitudes.
When Israeli officials asked Secretary Rice about the possibility of exploring the seriousness of Syria in its calls for peace talks, her response was unequivocal: Don't even think about it.
Israeli officials, including those in the intelligence community, are divided over the degree to which Syrian President Bashar Assad is serious and sincere in his call for peace talks with Israel.
One view describes Assad's call as a propaganda campaign, and insists that the Syrian leader is not serious. Among those holding this view is Mossad chief Meir Dagan.
In Military Intelligence the view differs. There are those who say that Assad is serious in his call for peace talks, but also say that this does not mean that those talks would be easy for Israel. They even suggest that there is a very good chance that the talks would fail.
It is also known that the Syrians have recently tried to send messages to the Israeli leadership through intermediaries in Europe. These are English nationals and former American diplomats.
The assessment is that the Syrian efforts are mostly the work of associates of Syria's foreign minister, Walid Mualem. The interlocutors approach various Israelis in order to cultivate ties with officials.
Prime Minister Ehud Olmert has so far adopted the strict American position not to respond to the Syrian feelers.
On the other hand, at the Foreign Ministry and within the defense establishment, there is a greater degree of openness to the offers, and the overall view is that the door should not be closed entirely to the Syrians. Similarly, many believe that the Syrian offers should be tested for their sincerity.
Among the leading individuals supporting this view is Defense Minister Amir Peretz.
Nonetheless, there is strict adherence to the principle of not acting against the views of the prime minister and of coordinating all matters with him.
At the Defense Ministry, they are aware that Syria is playing a very active role in Hezbollah's efforts to replenish its arsenal, and in particular its rocket stockpile. It appears that Hezbollah has already managed, since the war, to build up a stockpile of some 10,000 short-range rockets.
Syria assists Iran in arming Hezbollah with longer-range rockets.
According to one report, the Syrians have accepted an Iranian proposal for their agents to be more active in commanding the Hezbollah's long-range rocket forces.
Meanwhile, Peretz responded on Thursday to a story in Haaretz regarding Syrian efforts to rebuild its own military strength, saying that Israel should avoid making statements on developments in Syria.
Peretz was speaking at the weekly defense assessment in his office with senior officers in the defense establishment.
He said that there should be an effort to "avoid an escalation of words." The situation on the ground and along the border with Syria "will be evaluated on the basis of facts, and the IDF will prepare accordingly," he added.
The Haaretz report struck a chord in the Arab media, which gave it a leading position in its news and analysis items.
Three Syrian political analysts and politicians were interviewed on national television and denied the report on Syrian arms procurement and testing of ballistic missiles. However, all three emphasized that if there is no progress toward peace with Israel, then it is the "natural right" of Syria to take other types of action in order to liberate the Golan Heights.
Muhammed Habesh, a Syrian legislator, in an interview with the Al Arabiya satellite channel, said that "if Israel attempts to do something stupid, it will pay a hefty price for it."
He stressed that there has been no change in the border area in terms of the deployment of forces, and added that Syria was "ready for any eventuality."
It was also announced Thursday that 10,000 tons of apples will be delivered to Syria from the Golan Heights, under the auspices of the Red Cross.
The first three Red Cross trucks will cross into Syria on Monday morning. The transfer of the crop will continue for a period of 8-10 weeks. It is the third time a shipment of apples produced by Druze in the villages on the Golan Heights is being carried out, and it is expected to be the largest ever.