* Hamas wants end to Gaza blockade as part of truce terms
* Role of mediator see-sawing between rivals Qatar and Egypt
* Goals of Palestinian groups vary, but all disdain blockade
By Nidal al-Mughrabi and Noah Browning
GAZA, July 28 (Reuters) - After three weeks of intense fighting between Israel and Palestinian militants in the Gaza Strip, Hamas Islamists seem determined to wring clear concessions before halting fire.
A brief lull in the conflict on Monday to coincide with a Muslim holiday gave Gazans a rare chance to venture outdoors, but despite the death and devastation all around them, there was no sign of a clamour for an end to the battle.
Having suffered so much, many would see a truce that returned Gaza to the status quo under a stifling Israeli-Egyptian blockade as a defeat that could shred Hamas's already dented reputation at home.
"Hamas is at a crossroads: either it stops now and loses its popularity, or it continues and bears what war entails in terms of combat and martyrs to eventually achieve the people's demands," said Gaza analyst Hamza Abu Shanab.
"It looks to me like Hamas has decided to pursue the fight."
In many ways, Hamas has a lot to crow about from its 21-day confrontation with Israel -- certainly more than in the previous bouts of violence between the two in 2008/09 and 2012.
It has disrupted life across swathes of Israel with salvoes of missiles that briefly persuaded most foreign airlines to stop flying to Tel Aviv. It has improved battlefield tactics that led to the deaths of 43 Israeli soldiers -- almost four times the number killed in the last two conflicts.
In addition, Israel's global image has once more been tarnished as a result of a ferocious bombardment of Gaza that has killed almost 1,050 people, most of them civilians.
In the past, such achievements would have been enough for Hamas to declare victory and agree to a durable ceasefire.
But times have changed. Isolated within the Arab world and facing a financial crisis that has punctured its popularity, Hamas needs to be able to show its people concrete results from a conflict that has cost so many lives.
"We are determined to continue until all our demands are met," said a senior Hamas official, declining to give his name.
"We're in pain over the loss of so many civilians, over 1,000 innocent lives, but the souls of the martyrs will not have been lost in vain. The blockade that had claimed so many lives before, slowly, must now be lifted," he added.
While Israel says it has killed more than 200 Hamas fighters, the militants' command structure appears to remain intact and they continue to fire rockets into Israel daily, though in reduced numbers.
Israel says Hamas triggered the conflict through incessant rocket fire out of Gaza. This in turn followed a month-long arrest campaign against suspected Hamas members in the occupied West Bank after three kidnapped teenagers from a Jewish settlement were killed, in a crime Israel blamed on the Islamist group.
Israel says it does not deliberately target civilians and its Gaza campaign aims at staunching the rocket strikes and demolishing the militants' network of cross-border tunnels.
Gazans, fed up with dodging air strikes and dazed at the sight of whole neighbourhoods mangled by shelling, say their dedication to the armed "resistance" remains strong and accuse Israel of punishing civilians as a way of pressuring Hamas.
Although some no doubt feel angry with Hamas's government of Gaza, those feelings are not expressed at such sensitive times.
"We want 100 rockets to strike Tel Aviv at the same time to answer these massacres," said Ahmed Ramadan, standing in the rubble of houses in northern Gaza. "Victory is near ... after we have been suffocated all these years, we know the siege on Gaza will be broken," he added.
A diplomatic blitz last week by the United States and the United Nations with regional powers failed to secure a proposed seven-day truce, aimed at buying time for talks on easing the blockade and meeting Israel's security needs.
Israel's cabinet flatly rejected the idea and statements leaked by officials expressed fury at what they viewed as a U.S. capitulation to Hamas demands. Hamas sources said it had been inclined to accept the document.
Much of the gridlock boils down to rivalries unleashed by the revolts which rocked the Arab world in 2011, leading to the consolidation of two rival camps in the region.
Qatar and Turkey backed the upheaval's early beneficiaries in the Muslim Brotherhood - a region-wide Islamist political group which spawned Hamas - while Egypt, most Gulf countries and Hamas's secular Palestinian rivals in the Fatah movement view them as upstarts and distrust Hamas.
Egypt's military ousted the Muslim Brotherhood last year and proceeded to destroy hundreds of border smuggling tunnels that were the financial lifeblood of both Gaza and Hamas.
The move seriously reinforced an Israeli blockade in place since Hamas, which is sworn to Israel's destruction, won Palestinian parliamentary polls in 2006.
When Egypt proposed an immediate ceasefire on July 14 promising vague easings of its crossings with Gaza, Hamas said it had not even been consulted and its armed wing dismissed the plan as "an initiative of kneeling and submission".
Israel enthusiastically accepted.
When Egypt's effort foundered, the tiny gas-rich Gulf kingdom of Qatar raised its profile in the mediation, advocating on Hamas's behalf a fundamental change in Gaza's situation.
"The demands of our Palestinian brothers are fair and they are the minimum demands for a dignified life. What is needed in Gaza is to implement agreements from 2012 and 2011: find a commercial sea port for the people of Gaza so they can make a living and to waters as far as 12 miles," Qatari Foreign Minister Khaled Al-Atteya told Al Jazeera television on Sunday.
Attiyeh struck a conciliatory tone towards Egypt, suggesting that after the unsuccessful U.S. diplomacy, the responsibility for guaranteeing a truce fell to Cairo.
"(We) consider the role of Egypt is important and essential and ought to be in the forefront of this issue," he said.
Hamas has laid out a number of conditions for a truce, including the release of prisoners recently rounded up in the West Bank. However, its closest ally, Islamic Jihad, has made clear the overriding concern is the border closures.
"We are open to the Egyptian proposal and we seek to improve and modify it so it can include ending the blockade," Zeyad Al-Nakhala, the group's deputy head, said on Monday.
"Only a matter of days separate us from the end of the battle. The clouds will clear and you (Palestinians) will see victory," he told Al-Quds radio station.
The group mostly keeps out of factional politics and has less prestige at stake in outcome of the fighting than Hamas, which essentially runs the beleaguered Strip despite a unity deal it signed with Fatah in April.
Hamas's political leadership is scattered in Israeli prisons, Gaza, Egypt and Qatar, and its military wing appears less keen on talk of a truce. However, the multi-headed organisation still presents a united front.
A source in the group said its politicians were focused on the talks, while its fighters manned the front lines.
"(The political leadership) doesn't have to communicate with the military wing all the time. They have the demands and once they are met then a discussion could take place. Meanwhile, the fighters do what they're good at: fight," the source said. (Additional reporting by Amena Bakr in Doha; Editing by Crispian Balmer and Paul Taylor)