JERUSALEM (CNN) -- Israeli warplanes flew over the home of Syrian President Bashar al-Assad on Wednesday, as Israeli forces conducted operations in Gaza to save a kidnapped soldier.
The mission was the latest in a dramatic series of events raising tensions in the Middle East, including Israeli military raids into Gaza, where Cpl. Galid Shalit was believed to be held captive by groups linked with Syria.
The Israel Defense Forces confirmed that Israeli planes had flown over the Syrian president's palace and Israeli television reported Assad was at home at the time.
Israeli Deputy Prime Minister Shimon Peres has complained that Syria allowed the exiled political leadership of Hamas -- operating out of Damascus -- to order Shalit's kidnapping.
Three Palestinian militant groups said they were behind the 19-year-old corporal's kidnapping on Sunday: Hamas' military wing Izzedine al Qassam, the Army of Islam and the Popular Resistance Committees. The last group also claims to hold another hostage: 18-year-old Israeli settler Eliyahu Yitzhak Asheri.
Overnight Israeli aircraft hit Gaza's main electricity plant and key bridges that link the the Palestinian territory's northern and southern regions. (Watch a bomber's view of the airstrike -- 2:21)
Later on Wednesday Israel issued a warning to residents of northern Gaza to leave their homes. As dusk fell, Israeli tanks could be seen firing into the northern Gaza area, which Palestinians have been using for months to fire rockets at Israel.
Earlier raids were focused on the southern end of the territory.
The Hamas-dominated Palestinian Authority on Wednesday called for a swap with Israel -- Shalit in exchange for thousands of jailed Palestinians.
The PRC said the settler, Asheri, would be "butchered" unless Israel stopped its raid into southern Gaza.
In addition, The Associated Press reported that militants allied with Palestinian President Mahmoud Abbas' Fatah party claimed to hold a third captive, a 62-year-old Israeli from the central city of Rishon Lezion, whom they did not name.
Israeli police told AP that a 62-year-old man was missing, whom they identified as Noah Moskovitch.
Palestinian Prime Minister Ismail Haniya of Hamas told Reuters that Israel is worsening the crisis with its raids.
"We stress that the occupation must stop the military escalation in order not to complicate the situation and worsen the crisis," said Haniya.
"We are following the existing crisis relating to the missing soldier ... We hope that this case will be a concluded in a suitable way."
No casualties have been reported in the Israeli military raids, the largest since Israel pulled thousands of troops and settlers from Gaza last year after 38 years of occupation.
Taher Nono, a spokesman for the Palestinian Authority Foreign Ministry, said the ministry was calling on Arab governments to press for a "negotiated settlement" for the released of the Israeli soldier in exchange for jailed Palestinians, "especially women, children, the elderly and the sick prisoners" and long-term inmates.
The Palestinian Authority government said that Israel holds some 9,800 Palestinian prisoners.
Israeli Foreign Ministry Spokesman Mark Regev said to bargain with the Palestinian Authority over hostages would only result in more hostage incidents.
"People who take civilians and soldiers hostage and try to get ransom or to threaten us, it will not benefit them," Regev said. "It has to be a clear message, I think, from all democracies: If you take a hostage you are outside international norms, and you cannot expect to gain from hostage-taking."
Israel also conducted strikes on "open areas of southern Gaza Strip" on Wednesday.
The AP reported an Israeli airstrike on Rafah, Gaza, quoting witnesses who said two missiles fell about 200 meters apart, one in an empty training camp for Hamas. The other rocket hit an empty field nearby, and witnesses said they saw militants running away from the missile.
Israeli troops and armored vehicles crossed into southern Gaza early Wednesday, Israel's Defense Ministry said, with soldiers backed by artillery setting out from Kerem Shalom into Rafah.
The Israelis took up positions in Gaza shortly before 3 a.m. (8 p.m. ET) in the area where Shalit was abducted Sunday. Two other Israeli soldiers were killed in the weekend raid by Palestinian militants who tunneled into Israel.
Capt. Noa Meir, a military spokeswoman, said Israeli commanders have a "general idea" where Shalit was being held. (Watch the rescue operation begin -- 1:40)
Israel's Prime Minister Ehud Olmert told his parliament Tuesday to expect "an extended campaign against the Palestinian Authority" unless Shalit was released.
"All targets" would be considered for possible action, Olmert said the day after ruling out any deals with militants for Shalit's release.
