want bilateral recognition simultaneously based on 4th June, 1967 borders with return right of refugees. Palestinians want bilateral simultaneous agreement of non violence by both sides.
Hamas pays the price of principle
In the heat and dust of a packed Gaza City football stadium, the Palestinian Prime Minister and Hamas leader, Ismail Haniya, ended his latest big speech with a familiar promise.
He told the gathered masses again that Hamas would not recognise Israel - and they roared their approval.
And Hamas leaders do seem to believe that they can both retain their hard line on Israel and hold on to at least a share of power.
Hamas is under intense international and domestic pressure to moderate on the crucial recognition issue.
But Prime Minster Haniya's political adviser, Ahmad Yusuf, insists that the party can weather the storm.
The price of Hamas's refusal to renounce violence and accept Israel's right to exist has been economic and diplomatic isolation.
The United States and the European Union have severed all relations with the government.
Whatever pressure the world community will put on us, it will never make us give up our rights
Hamas political adviser
But Mr Yusuf is convinced that the Europeans are ready to come around.
All that is required, he says, is for the Palestinians to form a new government of national unity. That would bring Hamas into coalition with President Mahmoud Abbas's more moderate faction, Fatah.
Fudging the issue
Mr Abbas recently promised the United Nations and the world that any new administration would commit to all past Israeli-Palestinian agreements - which include recognition of Israel.
But Hamas says that he went too far.
"We have heard from a British source that once we have a unity government, maybe Prime Minister Haniya will receive an invitation from Tony Blair," said Mr Yusuf.
"I believe that the whole world will recognise this government - even if it doesn't recognise Israel."
Many have died in clashes between Hamas and Fatah supporters
And the Europeans have certainly indicated that they are ready to be flexible. It seems that they are open to a degree of fudging of the recognition issue.
Hamas may be reading far too much into those European signals. But what is important is that at its highest levels, Hamas clearly believes that it can stick to its line on Israel, and still hope to split the West.
But key to that strategy is the formation of a government of national unity - and for now at least, that effort is going nowhere.
President Abbas wants an administration with an agenda that would at least implicitly endorse Israel's existence in a way that would bring a complete end to the international embargo.
In Fatah's eyes, signing up to anything less would risk buying into a government that would fail.
Fatah would share the blame, and might be subjected to the some of the same US sanctions that Hamas endures.
Hamas meanwhile has searing contempt for what it regards as Fatah's collusion with Washington.
And if the differences between the two parties make it impossible to form a unity government, then Mr Yusuf says his party can tough out the rising pressure.
Civil servants have taken to the streets over unpaid wages
Its refusal to recognise Israel lies at the heart of the party's ideology. It sees itself as defending the right of Palestinians to return to ancestral lands - God-given Muslim lands - that were lost in the war of 1948.
"We are not going to surrender our rights for bread," Mr Yusuf says. "We have dignity, rights - we have lands and property.
"Whatever pressure the world community will put on us, it will never make us give up our rights."
He argues that Palestinians have been hardened to suffering by decades of poverty and Israeli occupation, and that they can endure the additional hardships of the current situation.
The Palestinian economy is being hit very hard by Israeli and American sanctions.
But significant financial and other assistance is still coming.
Major United Nations aid programmes remain unaffected, and many tens of thousands people have been added to food hand-out lists.
Founded in 1987
Listed as a terrorist group by US and EU
Combines military and political wings
Political wing has a majority in Palestinian parliament
Founding charter calls for the elimination of Israel
And although the EU is boycotting the Hamas government, it is channelling more money than ever through Mr Abbas and the presidency.
The government is in such a desperate financial situation that it suspended regular salary payments about seven months ago.
But there have been a series of small payments.
They have only constituted a third or less of the pay of the upper and middle-ranking civil servants. But these are people traditionally associated with support for Fatah - and Hamas's concern for them is perhaps limited.
Meanwhile, the lower ranks, who of course earn less, have received a much higher percentage of their wages.
"We believe that we will have enough money to survive," Mr Yusuf says.
He also believes that Hamas is on secure legal ground in its confrontation with Fatah.
President Abbas can dissolve the Hamas government, but any administration that replaces it has to be approved by parliament - where Hamas has a majority.
And while some in Fatah urge the president to call early elections, independent legal analysis backs the Hamas view that the constitution does not give Mr Abbas that power.
Hamas hopes to increase its influence while retaining its support
The acute political tension has already led to an outbreak of street fighting.
Some fear a civil war, but Mr Yusuf insists that it will not come to that.
"In each family you will find people from Fatah and Hamas," he said. "I am from a family that has all the Palestinian political and military factions in it. We will never fight each other."
And even if the worst were to happen and there was major violence, Hamas - in Gaza at least - is far too strong to be swept away militarily.
On several fronts then, Hamas believes that it can take the pressure.
The movement sometimes seems to thrive on crisis, and it is often a mistake to underestimate it.
But as the weeks slip by, the political and economic tensions grow ever more acute and dangerous.
And Hamas may find itself paying an increasingly heavy price in terms of public opinion.
Even in its heartland, the refugee camps of Gaza, there is already real disappointment that the party that came to power promising "change and reform" has so far been able to deliver only crisis and paralysis.
As a recent report by the International Crisis Group put it, there is a weariness with Hamas's commitment to "principle over pragmatism".