Gaza: What Comes Next, Truce or Ground Invasion?

As the Israeli offensive heads into its sixth day and the missile strikes in Gaza continue, the international community has increased the volume on its call for a cease-fire.

Israeli warplanes struck 20 targets in Gaza overnight. The Israeli Air Force widened its targets to include Hamas' political institutions, its parliament and the Ministry of Justice. Israeli planes also hit the tunnels used for smuggling on the Gaza-Egypt border.

"Hamas government sites serve as a critical component of the terrorist groups' infrastructure in Gaza," Israel's Defense Force said in a statement.

An Israeli airstrike today hit the house of senior Hamas leader Nizar Rayyan, killing him, his wife and three children. Rayyan had refused to leave his house since the beginning of the Israeli offensive Saturday.

As of now, 26 Hamas rockets have been fired at Israeli cities. One was a direct hit on a residential building in Ashdod, about 17 miles north of Gaza. There were no casualties.

This afternoon, the Israeli Air Force struck the underground launching post from which the rocket that hit Ashdod was launched. Israeli planes also targeted several weaponry storage facilities in Gaza.

Hamas Prime Minister Ismail Haniyeh spoke on local TV Wednesday night for the first time since hostilities broke out, detailing his conditions for a cease-fire.

"First, Israel must stop the aggression, lift the siege on Gaza and open the border crossings," he said, speaking from a bunker somewhere in the Gaza Strip.

Israeli Foreign Minister Tzipi Livni, who is a contender in next month's election to become Israel's prime minister, rejected any cease-fire, saying such a move at this time would only benefit Hamas.

In an interview with ABC News' chief Washington correspondent George Stephanopoulos, Livni said the cease-fire was unnecessary because Israel is keeping the border "crossings open during this operation" to allow "humanitarian aid to enter the Gaza Strip."

Inside Gaza humanitarian conditions are getting worse, with people waiting hours for bread alone. The number of dead in Gaza has risen to an estimated 400, with 2,000 injured. The U.N. special representative told ABC News Wednesday that the number of dead was between 320 to 390 -- 20 percent to 25 percent of them women and children.

Israelis Favor Strikes

Diplomatic activity to stop the fighting is gaining pace but so is the momentum for an Israeli ground invasion. One Israeli officer told ABC News this morning, "If anyone thinks that we are going to behave gently, they are wrong."

A poll conducted by the influential Israeli newspaper Haaretz showed that 52 percent of Israelis are in favor of continuing the airstrikes but that 19 percent favor a ground invasion. Twenty percent of Israelis said the country should declare a cease-fire as soon as possible.

The Haaretz-Dialog poll also showed that Israeli Defense Minister Ehud Barak, leader of the diminished Labor Party and most credited with the military offensive, is gaining most in the polls.

A week before the offensive, polls showed Labor winning 10 seats in elections to be held Feb.10. Today's poll shows the same party winning 16 seats.

Perhaps in a bid to better Barak's chances even further, the influential Israeli Web site YNET reported that Barak was moving his house from Tel Aviv to Israel's southern Negev region, which has been under constant barrage from Hamas rockets.

Israeli security sources told ABC News that the move is being considered but that the Ministry of Defense had no comment on the matter.

The location of the house would be secret for security reasons but the head of the regional council in which the house reportedly sits told YNET, "Barak told me he fell in love with the region and that he's moving here. … Talking to him I got the impression he really likes it here, I don't think it's a gimmick of some sort."

U.S. Rejects Resolution

At the United Nations in New York, the United States rejected an Arab-sponsored, legally binding Security Council resolution that would have ensured an immediate cease-fire.

The United States called it too one-sided for not taking into account Hamas rockets that have harassed citizens of southern Israel for years.

After the resolution's failure, U.N. Secretary-General Ban Ki-moon tried to bridge both sides, saying, "Let me be clear, I condemn unequivocally, and in the strongest possible terms, the ongoing rocket and mortar attacks by Hamas and other Palestinian militants. But I also condemn the excessive use of force by Israel. All parties must fully uphold international humanitarian law."

Nasser Atta, Matthew McGarry, Simon McGregor-Wood and Dana Savir contributed to the reporting of this story.