EREZ CROSSING, on the Israel-Gaza border — As Israel’s tanks and troops poured into Gaza on Saturday, the next phase in its fierce attempt to end rocket attacks, a question hung over the operation: can the rockets really be stopped for any length of time while Hamas remains in power in Gaza?

And if the answer is determined to be no, then is the real aim of the operation to remove Hamas entirely, no matter the cost?

After her visit to Paris on Thursday to explain to French authorities why she thought this was not the time for a quick cease-fire, Foreign Minister Tzipi Livni of Israel said, “There is no doubt that as long as Hamas controls Gaza, it is a problem for Israel, a problem for the Palestinians and a problem for the entire region.”

Vice Premier Haim Ramon went even further Friday night in an interview on Israeli television, saying Israel must not end this operation with Hamas in charge of Gaza.

“What I think we need to do is to reach a situation in which we do not allow Hamas to govern,” Mr. Ramon said on Channel One. “That is the most important thing.”

Neither Prime Minister Ehud Olmert nor Defense Minister Ehud Barak has made such a statement. Still, there is a growing and shared concern among Israeli leaders that any letup against Hamas would be problematic for Israel’s broad goals in the long term because it could bolster and validate the group, which says Israel should be destroyed.

“If the war ends in a draw, as expected, and Israel refrains from re-occupying Gaza, Hamas will gain diplomatic recognition,” wrote Aluf Benn, a political analyst, in the newspaper Haaretz on Friday. “No matter what you call it,” he added, “Hamas will obtain legitimacy.”

In addition, any potential truce deal would probably include an increase in commercial traffic from Israel and Egypt into Gaza, which is Hamas’s central demand: to end the economic boycott and border closing it has been facing. To build up the Gaza economy under Hamas, Israeli leaders say, would be to build up Hamas. Yet withholding the commerce would continue to leave 1.5 million Gazans living in despair.

Implicit in Mr. Benn’s argument, however, is that the only way to stop Hamas from gaining legitimacy is for Israel to fully occupy Gaza again, more than three years after removing its soldiers and settlers. That is a prospect practically no one in Israel or abroad is advocating.

Moreover, while it may sound decisive to speak of taking Hamas out of power, almost no one familiar with Gaza and Palestinian politics considers it realistic. Hamas legislators won a democratic majority in elections four years ago, and the group has 15,000 to 20,000 men under arms. It has consolidated its rule in the past 18 months since pushing out its rivals loyal to the more Western-oriented and moderate Fatah party of President Mahmoud Abbas, who sits in Ramallah in the West Bank.

And while there are plenty of Gazans who would prefer Fatah, they seem hardly organized or strong enough to become the new rulers, even with the help of former colleagues in exile in Ramallah who say, anyway, that they would never be willing to ride into Gaza on the back of an Israeli tank. In fact, the longer Israel pounds Gaza, the weaker Fatah is likely to become because it will be seen as collaborating.

The likelier result of a destruction of the Hamas infrastructure, then, would be chaos, anathema not only to the people of Gaza but also to those hoping for peace in southern Israel.

Yet in its campaign so far, which has killed scores of children and other bystanders, Israel has not spared the trappings of Hamas sovereignty or limited itself to military targets. It says that the mosques it has destroyed were weapons storehouses and that the Islamic University, which it has hit repeatedly, housed explosives factories. But it has also reduced many government buildings to rubble without any claim that they were military in nature.

“The government buildings are a place where financial, logistical and human resources serve to support terror,” said Capt. Benjamin Rutland, a spokesman for the Israeli military. “Much of the government is involved in the active support and planning of terror.”

Taken together, it suggests that even if Israel intends to hold back from completely overthrowing Hamas, its choice of assault tactics could head that way anyway. And the Israelis may already be facing a kind of mission creep: after all, if enough of Hamas’s infrastructure is destroyed, the prospect of governing Gaza, a densely populated, refugee-filled area whose weak economy has been devastated by the Israeli-led boycott, will be exceedingly difficult.

In the background, too, is broad international criticism of this war on Gaza, not only because of the unspeakable suffering seen on television screens but also because of a feeling that Israel has tried such tactics in the past and never succeeded.

In particular, many point to the 2006 war against Hezbollah in Lebanon, where Israel also tried to destroy rocket launchers and a hostile organization’s infrastructure, only to end up killing many civilians and leaving Hezbollah more popular and perhaps ultimately stronger than before the war.

But military planners here say that the parallel is inexact and that they, too, have learned a lesson. Gaza is smaller and flatter than southern Lebanon and, most important, does not have a sievelike border with a country like Syria where arms can be constantly resupplied. Destroying the smuggler tunnels from the Egyptian Sinai into Gaza and systematically eliminating weapons depots and launcher sites, along with their supporting infrastructures, will ultimately succeed, they contend.

It may take weeks or months, they assert, but it can work. If true, questions still remain: At what human cost? And who will be in charge when it is all over?