CAIRO, Egypt – By dispatching two fighter jets yesterday to buzz the summer palace of President Assad, Israel sent a clear warning to Syria that it holds the Damascus regime responsible for the safe return of a kidnapped soldier and a settler.

The flyover was a sharp response to mounting frustration at Syria’s role in harboring the head of Hamas’s politburo, Khaled Meshaal, and to reports that Mr. Assad has been pressing Hamas to refuse requests from Egyptian envoys to hand over to Israeli authorities 19-year-old Corporal Gilad Shalit, who was kidnapped by Hamas terrorists near southern Gaza over the weekend.

Mr. Assad’s international standing was not improved yesterday after he refused a telephone call from Secretary-General Annan urging him to use his influence to help release the Israeli soldier, according to one Western diplomat.

Hamas admitted for the first time yesterday that it has influence over the fate of Corporal Shalit when it offered a swap of the soldier for Palestinian Arab political prisoners.

Prime Minister Olmert summarily refused the offer, promising harsher measures if the soldier and the settler, Eliahu Asheri, 18, who was kidnapped on the West Bank on Tuesday, were not returned safely. Israeli tanks rolled into southern Gaza near the Rafah border crossing early Wednesday morning and took out three bridges and an electrical relay station in an effort to capture their missing soldier.

“Israel will not balk at extreme action,” Mr. Olmert said.

The fighter jets’ low swoop over Mr. Assad’s summer palace was the first Israeli incursion into Syrian airspace since 2003, when Israeli jets flew so low and fast over the palace that the building’s windows reportedly shattered. In October 2003, Israel bombed a Palestinian Islamic Jihad training camp in Syrian territory in response to a suicide bombing by the group that killed 19 Israelis.

The latest round of fighter jet diplomacy was meant as a direct message to the Syrian leader to end his meddling in the Gaza powder keg. In the last year, Israel has absorbed close to 1,000 rocket attacks on its southern border with Gaza, Israeli officials said. In April, Jordanian authorities intercepted an arms cache its officials said was shipped from Syrian territory and intended for Hamas terrorists.

An Israeli official in Washington said yesterday that Mr. Meshaal was “personally responsible for the operation, the kidnapping, and personally responsible for not releasing the soldier.” The official, who requested anonymity, added: “We are sending a clear message to Damascus. There is no difference between aiding and abetting terror and being a terrorist.”

While American officials did not endorse Israel’s actions openly yesterday, they did not condemn them. The White House press secretary, Tony Snow, and a State Department spokesman, Adam Ereli, both reiterated, “Israel has a right to defend itself and the lives of its citizens.” Both added the caveat that they hoped civilian lives would be protected in the Israeli military operation to recover the kidnapped Israelis.

The re-entry of Israeli troops into Gaza in the last 48 hours represents the most direct military response from the Jewish state since Mr. Olmert became prime minister, and also re-establishes that when Israel can show a direct connection between Syria and attacks on its citizens, it will not hesitate to violate the country’s airspace.

Opponents of the Syrian leader greeted the flyover enthusiastically yesterday. A former Syrian vice president turned star witness in the U.N. inquiry into Syria’s role in the murder of a former Lebanese prime minister, Abdel Halim Khaddam, featured the story at the top of his Web site.

“This is indicative that not only Israel is running out of patience with the terrorism that is planned in Damascus, but we believe the United States may not at all dislike what happened,” the president of the Reform Party of Syria, Farid Ghadry, said. “The message to Assad is, ‘Clear your plate of terrorism or we will come after you.’ This is very encouraging to the Syrian opposition.”

Mr. Ghadry met with Vice President Cheney on June 17 at the American Enterprise Institute’s annual retreat in Beaver Creek, Colo.

A research fellow at the Foundation for the Defense of Democracies, Tony Badran, said Syria’s recent behavior is evidence of its alignment with Iran, Hezbollah, and Hamas.

“Given how the Jordanians thought the Hamas arms cache came from Syria, it would not surprise me if the Syrian-based Hamas is behind the operation,” Mr. Badran said. “The Israelis are saying there is a direct link. This shows how entrenched Syria is in the Iran-Hamas-Hezbollah axis.

“This reinforces the perception that Syria is going against the policies of the regional powers. While Jordan and Egypt are trying to moderate Hamas, Syria is pushing Hamas to be more hard line,” he said.

[The Associated Press reported last night that the Popular Resistance Committees, a Palestinian Arab terrorist group, released a statement saying it had killed Mr. Asheri, the Israeli civilian who was being held hostage. His body was reportedly found in Ramallah, a city in the West Bank, Palestinian Arab security officials said.

Increasing pressure on Hamas, Israeli forces arrested more than 30 lawmakers yesterday, according to Palestinian Arab security officials. Among those detained were the Palestinian Arab deputy prime minister, Nasser Shaer, the labor minister, Mohammed Barghouti, and two other ministers in the West Bank.

The security officials said two others were arrested in the town of Jenin, and Israeli press reported a roundup of Hamas lawmakers in Jerusalem and other locations.]