Israeli artillery continued shelling areas in the Gaza Strip
Israeli forces in Gaza
The detainees include eight members of the Hamas-led government and 20 MPs. Palestinians called it an act of war.
The Israelis say they suspect them of involvement in terrorism, and are holding them for questioning.
Foreign ministers of the G8 countries meeting in Moscow called on Israel to exercise utmost restraint.
Israeli military units advanced into southern Gaza on Tuesday night as part of efforts to get the soldier, Corporal Gilad Shalit, released.
They are not bargaining chips for the return of the soldier - it was simply an operation against a terrorist organisation
Israeli army spokeswoman
Gaza infrastructure suffers Gaza voices: Thursday
Much of Gaza has been left without electricity and running water after a power plant was hit by Israeli missiles on Tuesday.
Israel aircraft also destroyed several bridges, preventing travel between the north and south of the 45km (30-mile) Strip.
The body of a teenage Israeli settler abducted by Palestinian militants on Sunday has now been recovered by Israeli troops near the West Bank town of Ramallah.
'War of terror'
Israel has said it will not negotiate Cpl Shalit's release with his captors, or free Palestinian women and children held in its jails, as the militants demand.
Gaza Strip in detail
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"They are not bargaining chips for the return of the soldier - it was simply an operation against a terrorist organisation," said an Israeli army spokeswoman.
As they called for calm, the G8 foreign ministers were among a number of international bodies to question Israel's move.
"The detention of elected members of the Palestinian government and legislature raises particular concerns," the ministers said in a written declaration.
They also demanded the immediate release of Cpl Gilad - who was seized by Palestinian militants during a raid on an army post outside Gaza on Sunday.
"We are united in demanding that the Israeli soldier be freed as soon as possible," Russian Foreign Minister Sergey Lavrov said at a news conference.
We are living, but we feel as if we are dead
Doaa Abu-Harb
Student, Rafah
In pictures: Strike aftermath In quotes: World reaction
Meanwhile Syria condemned an incursion by at least two Israeli war planes into its airspace on Wednesday, flying over the summer residence of President Bashar al-Assad.
Israeli officials accuse the Syrian government of harbouring the political leadership of Hamas, which it blames for the seizing of Cpl Shalit.
Dug in
The Israeli military detained more than 64 Hamas officials and parliamentarians in overnight raids across the West Bank.
The detained ministers include Finance Minister Omar Abdal Razeq, Social Affairs Minister Fakhri Torokma and Prisoners' Affairs Minister Wasfi Kabha and Deputy Prime Minister and Education Minister Nasser Shair.
CAPTURED ISRAELI SOLDIER Cpl Gilad Shalit, 19 First Israeli soldier captured by Palestinians since 1994
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The Israeli air force staged mock raids over Gaza, causing sonic booms, and dropped leaflets in northern Gaza urging residents to avoid moving in the area because of impending military activity.
Israel aircraft later attacked a car in Gaza City carrying militants from the Islamic Jihad group, Palestinian sources said.
The militants escaped, although one was lightly injured in the blast, witnesses said.
Nervous civilians stockpiled batteries and candles, as well as food and water.
In southern Gaza, where the Rafah crossing with Egypt has been closed since Cpl Gilad's capture, militants blew a large hole in the border wall.
Palestinian security forces stopped people from pushing through the gap by forming a human cordon, and a curfew was imposed.
A 3,000 strong detachment of the Israeli Defense Forces has moved back into the Gaza Strip only months after withdrawal of settlements from the area. Eight Hamas cabinet ministers, in addition to other officials, have been detained in a coordinated action codenamed Operation Summer Rains. The pre-planned operation was launched in immediate response to what Israel said was the kidnap of 19-year-old Israeli tank gunner Cpl. Gilad Shalit on 25 June.
Map of the Gaza Strip.
Three bridges in the Gaza Strip have been bombed for the stated purpose of restricting the movement of the hostage takers and the hostage. 

In other operations a helicopter attack on a power station in Gaza plunged large portions of the Gaza Strip into darkness, leaving somewhere around 700,000 civilians without electricity or water. While Israeli troops and armored vehicles, lead by bulldozers, also moved into Gaza near a disused international airport. 

There were also reports of Israeli warplanes making warning flights over Syria in what has been reported to be a warning "against supporting Palestinian militants."

"Fight your enemies, who came to their deaths. Grab your rifles and resist," said Nizar Rayan in a radio message to Palestinian militants. Despite this exhortation, there were no immediate reports of casualties or conflicts.

"We have no desire to remain in the Gaza Strip," said Israeli National Infrastructure Minister Binyamin Ben-Eliezer, on  Israel Radio, although he did not give a timetable for the operation. "We want to bring our boy home, that's all."

The Popular Resistance Committees threatened to kill an Israeli soldier, kidnapped in the West Bank. The body of an 18-year-old Israeli settler, Eliyahu Yitzhak Asheri, kidnapped while hitchhiking in the West Bank, was found in the A-Tira neighbourhood of Ramallah today; he was killed by Palestinian militants from the Popular Resistance Committees on Sunday. 

Israel has also detained dozens of Hamas MPs and ministers in a what Israel claims is an unrelated operation. An Israeli official denied the capture as a use for bargaining with the kidnappers saying, "They are not bargaining chips for the return of the soldier - it was simply an operation against a terrorist organisation."