Three years after Hamas seized control of the Gaza Strip in a bloody battle with its secular rival, Israel's efforts to undercut the Islamist movement's rule through a policy of isolation have largely failed, according to analysts and residents here.

Hamas's security forces remain strong and in full control, while more extreme Islamist challengers are gaining influence because of an Israeli embargo that has done more to frustrate the population than to weaken Hamas's grip, analysts say.

Before Israeli commandos killed nine activists in a confrontation aboard a Turkish aid ship bound for Gaza last week, Israeli officials were largely content with their policy toward the territory. Hamas was in a box, they said, and had been deterred since early last year from firing rockets into Israeli towns after a brief, lopsided war in which about 1,400 Palestinians were killed. Israel saw no reason to relax the siege in substantive ways, preferring instead to wait and see whether Gaza's residents would rise up and force Hamas out.

But even if Gazans wanted to revolt -- and there is little evidence they do -- they probably would be unable to do so, given Hamas's clout. Thousands of security personnel police the sliver of territory along the Mediterranean Sea, performing an array of functions such as intelligence gathering, conducting traffic and policing morality.

Cut off from international commerce, Hamas is sometimes short on cash. But the movement garners revenue through taxes, a black market economy tied to smuggling and donations from international sponsors such as Iran. Along with millions of dollars, thousands of rockets have been transported through tunnels beneath the border with Egypt.

Israel's restrictions on Gaza have boosted Hamas's popularity throughout the Middle East, a trend that may have been accentuated by last week's confrontation at sea.

"Part of the goal of the siege was to pressure the population so it would act against Hamas. This has not happened, and this will not happen," said Mukhaimer Abu Saada, a political science professor at Gaza's al-Azhar University. "Hamas has become militarily more powerful and has used violence against its opponents. Rising up against Hamas is not an option, and people are not thinking about it."

If Hamas faces any real competition, it comes not from relative moderates such as the rival Fatah party, but from those who are even more ardently Islamist than Hamas itself and are pushing for a broader, al-Qaeda-like holy war. These more extreme challengers, though limited in number, think that Hamas is not moving fast enough to impose an Islamic code of life in Gaza.

Bruce Riedel, a former Middle East analyst for the CIA who is now with the Brookings Institution in Washington, said he has no doubt that "Hamas now faces a much bigger threat from the extreme jihadists sympathetic to al-Qaeda" than from Fatah, which controls the West Bank. Al-Qaeda sympathizers appeal to Hamas's core constituency "of militants who want to fight Israel, not live in a cease-fire and under blockade. They are frustrated that Hamas won't allow [rocket] attacks or attempts to kidnap more Israelis. Hamas has the upper hand for now because it has more force and is ruthless in using it, but the long trend is worrisome."

Hamas, which the United States considers a terrorist organization, carried out scores of suicide bombings and other deadly attacks on Israeli civilians in the past two decades. With Hamas unable to send bombers into Israeli cities with the tightening of the blockade in 2007, rockets became the main form of violence until the war in Gaza. Since the three-week war ended in January 2009, there has been a lull in rocket fire, leading some to suspect that Hamas is rebuilding its arsenal.

The Islamist movement has tried through dialogue and force to deal with more radical jihadists. Last summer, Hamas security forces killed 21 members of an outlawed fundamentalist group after its leaders declared the establishment of an Islamic emirate in the southern Gaza city of Rafah.

Mahmoud Zahar, a Hamas founder, dismissed the radical groups in an interview, saying that the biggest threat to his organization remains "the collaborators with Israel." But other Hamas leaders say that the strengthening of radical sentiment in Gaza is one reason the West should be concerned about Israel's blockade of Gaza and that dialogue with Hamas is the answer. "The Western world should decide if they want to deal with the true Islam or these fundamentalists," said Khalil al-Haya, a top Hamas figure.

While some Hamas leaders appear to be searching for a strategy that ends their isolation, those efforts have been undermined by thuggish behavior from other elements of the group. As the aid flotilla was seized by Israel last Monday, Hamas's security services ransacked the offices of nongovernmental organizations that work on behalf of children. Last month, masked vandals tied up a security guard and torched a summer camp run by the United Nations. Before the attack, members of an unknown group distributed leaflets protesting the camp's planned offerings of dance and art, as well as the mixing of boys and girls at the facility -- even though they would be attending camp at different times of day.

Hamas said it arrested suspects. But some political observers in Gaza suspect Hamas may have ordered the vandalism itself amid fears that the camp posed a challenge to the group's summer camps, which stress the study of the Koran and form a core part of Hamas's youth indoctrination.

"An environment has been created that resulted in this," said Issam Younis, head of the Gaza-based al-Mezan Center for Human Rights. "Whether these people are a wing of Hamas or from the outside is beside the point."