An Israeli airstrike Saturday killed a senior Hamas commander, Reuters reported.
Hamas said the airstrike in Gaza killed Abu Zakaria al-Jamal, a senior leader of the armed wing of the militant group.
The Israeli army would only say it carried out a series of air attacks through the night.
Israeli warplanes and gunboats blasted more than two dozen Hamas targets Saturday, including weapons storage facilities, training centers and leaders' homes as Israel's offensive against Gaza's Islamic militant rulers entered a second week.
The Jerusalem Post reported the home of al-Jamal was a target of the raids. He was the third senior Hamas operative to be targeted.
In a strike Friday the Israeli Air Force bombed the house of top Hamas operative Imad Akel. The Israeli military reported hearing secondary blasts at the house, indicating the presence of a stash of weapons and explosives in the home, the Jerusalem Post reported.
On Thursday an Israeli warplane dropped a 2,000-pound bomb on the home of one of Hamas' top five decision-makers, instantly killing him and 18 others.
The airstrike on Nizar Rayan was the first that succeeded in killing a member of Hamas' highest echelon since Israel began its offensive.
The Jerusalem Post also reported Saturday that Hamas declared its members foiled an attempt by Israeli forces to move within the Gaza Strip.
Hamas claimed the soldiers retreated after they were targeted by mortar shells.
Israeli forces, however, claimed the "incident never happened."
Senior leadership in Israel had given the thumbs up for a ground invasion of the Gaza Strip, sources told FOX News, though it didn't mean such action was inevitable.
A ground invasion could happen soon if international diplomacy fails to broker a cease-fire between Israel and Hamas, who have been trading cross-border fire for the past week.
As ground troops massed on the border Saturday, waiting for a signal to invade Gaza, the cease-fire efforts were gaining momentum.
French President Nicolas Sarkozy is visiting the region next week, and President George W. Bush and U.N. chief Ban Ki-moon both spoke in favor of an internationally monitored truce.
Israel launched its new round of airstrikes on Gaza in response to renewed missile attacks by Hamas after the two sides' six-month cease-fire ended last month. A ground invasion of the territory has looked increasingly likely, as Israel has been bringing artillery, armor and infantry to the border.
Israel bombed a mosque it claimed was used to store weapons and destroyed homes of more than a dozen Hamas operatives Friday, but under international pressure, the government allowed hundreds of Palestinians with foreign passports to leave besieged Gaza.
Exiled Hamas leader Khaled Meshaal said from Damascus on Friday that his militant group was prepared for an invasion and could abduct more soldiers if Israel attempts the incursion.
"If you commit a foolish act by raiding Gaza, who knows, we may have a second or a third or a fourth Shalit," he said, according to Reuters. Israeli soldier Gilad Shalit was kidnapped by Hamas in a cross-border raid more than two years ago.
Hamas, whose charter specifically calls for the destruction of the state of Israel, had ordered a "day of wrath" against Israel on Friday over the killing of a senior commander.
In last 48 hours, the U.S. government has helped 27 Americans get out of Gaza, and has heard no reports of any Americans being injured during the assault, according to State Department spokesman Gordon Duguid. Evacuated Americans were taken by bus to Amman, Jordan, but more Americans are believed to be in Gaza.
President Bush, in a radio address taped Friday, accused Hamas of an "act of terror" in its rocket attacks into Israel and suggested that no cease-fire would be acceptable without monitoring to halt the flow of weapons to terrorist groups.
Israel launched the aerial campaign last Saturday in a bid to halt weeks of intensifying Palestinian rocket fire from Gaza. The offensive has dealt a heavy blow to Hamas, but failed to halt the rocket fire. New attacks Friday struck apartment buildings in the southern Israeli city of Ashkelon, though no serious injuries were reported.
The United Nations estimated Friday that around 100 civilians have been killed in Gaza in the past week, around 25 percent of the 400 estimated killed in the bombing campaign.
The Israeli military called at least some of the houses ahead of time to warn inhabitants of an impending attack. In some cases, it also fired a sound bomb to warn away civilians before flattening the homes with powerful missiles, Palestinians and Israeli defense officials said.
Three Israeli civilians and one soldier have also died in the Hamas rocket attacks, which have reached deeper into Israel than ever before, bringing one-eighth of Israel's population of 7 million within rocket range.
Hamas is listed as a terrorist organization by the United States and many other Western nations. From 2001 through May 2008, Hamas launched more than 3,000 Qassam rockets and 2,500 mortar attacks against Israeli targets.
FOX News' Mike Tobin and the Associated Press contributed to this report.