Few game-changing proposals are emerging to defuse tensions in the Middle East as a busy week of diplomacy unfolds with President Obama’s address to the region and his meeting with Israel’s prime minister.

Against the backdrop of Middle East uprisings that have intensified animus toward Israel and growing momentum for global recognition of a Palestinian state, American and Israeli officials are struggling to balance national security interests against the need to adapt to a transformative movement in the Arab world.

The White House unveiled a $2 billion multiyear economic aid package for Egypt, which officials say would largely shift existing funds. Prime Minister Benjamin Netanyahu of Israel prepared to arrive in Washington with a package that he hoped would shift the burden of restarting the peace process to the Palestinians.

Mr. Obama, who is set to address Americans — and, more significantly, Muslims around the world — from the State Department on Thursday morning, may yet have something surprising up his sleeve. One administration official said that there remained debate about whether Mr. Obama would formally endorse Israel’s pre-1967 borders as the starting point for negotiations over a Palestinian state, a move that would send an oratorical signal that the United States expected Israel to make concessions.

But Mr. Obama did not plan to present an American blueprint for peace, White House officials said, and it remained unclear if he would even endorse a Palestinian state on pre-1967 lines, a move opposed, administration officials said, by his chief Middle East adviser, Dennis Ross. Mr. Obama did seek to increase pressure on Syria by imposing largely symbolic sanctions on its leader, President Bashar al-Assad, in the wake of the bloody crackdown there.

White House officials declined to say whether Mr. Obama would go further in Thursday’s speech and call on Mr. Assad to resign.

The debate around Mr. Obama’s remarks, which the White House has billed as a major address, is made even more significant since the president’s speech will serve as the beginning of what promises to be several intense days of debate over American policy in the region, its support for Palestinian statehood, and how far Mr. Obama is willing to push Israel on peace with the Palestinians at a time of upheaval in the region. Mr. Obama is to meet with Mr. Netanyahu the day after his speech, on Friday. Two days after that, Mr. Obama is scheduled to address the American Israel Public Affairs Committee, the pro-Israel lobby. Next week, Mr. Netanyahu will counter with his own address to a joint meeting of Congress.

Mr. Netanyahu, aides say, is planning to tell Mr. Obama that Israel wants to keep a military presence along the Jordan River and sovereignty over Jerusalem and the settlement blocs — three major stumbling blocks for the Palestinians — but that it would be willing to negotiate away the rest of the West Bank, more territory than Mr. Netanyahu has been willing to specify in the past. He has one condition — the Palestinian government cannot include Hamas. Mr. Netanyahu knows that the Palestinians will find this condition unacceptable, particularly since Fatah, the main Palestinian movement, just signed a unity pact with Hamas. But since the United States labels Hamas as terrorists, Mr. Netanyahu is betting that he will appear more forthcoming than ever.

“On the one hand, the Palestinians are moving toward Hamas while on the other, the prime minister is showing a real willingness to make far-reaching territorial compromise,” a top Netanyahu aide said, speaking on condition of anonymity.

Whether Mr. Netanyahu’s offer, first outlined in a speech to Parliament on Monday, is a genuine attempt to negotiate peace with the Palestinians, or to make it appear that the Palestinians are the ones blocking progress, is not yet clear. The Palestinians want East Jerusalem as their capital and do not want Israeli soldiers along the Jordan.

Diplomatic momentum has been with the Palestinians for several years, with their leadership and requests viewed as reasonable and Mr. Netanyahu as unyielding. Some in Israel believe now is the time to seize the moment with a bold initiative, but they are not in power. “The coming days are a final chance to stop or at least to slow Israel’s diplomatic decline,” Dov Weissglas, who was bureau chief for Ariel Sharon when he was prime minister, wrote in Wednesday’s Yediot Aharonot newspaper. He wants a more far-reaching offer from Mr. Netanyahu that would give up East Jerusalem and not require that Israel keep soldiers along the Jordan.

While there are Israeli scholars and former officials who believe that Hamas, which rules Gaza, could become more moderate, the dominant intelligence estimate in Israel is that Hamas will not change. “We have a strong body of evidence showing that while Hamas has grown pragmatic, it is not moderate,” a senior Israeli defense official said, speaking on the condition of anonymity. “It is far more likely that Hamas will take over the Palestinian Authority than vice versa.”

Many, including some within the Obama administration, think the talks with Hamas need not be a deal breaker and could even be useful over the long run. Finally, the upheavals in the Arab world are turning the mood ever more against Israel, making American and European leaders eager to pressure it for concessions.

So far Mr. Obama has not used the moment to push Israel. But Palestinians have been absorbing lessons and audacity from pro-democracy demonstrators across the Arab world. They have learned the value of unarmed mass movements organized on Facebook and other social media.

Last Sunday, thousands of Palestinians approached Israel’s borders to claim, at least symbolically, their right of return on the anniversary of Israel’s founding. Israeli troops opened fire and more than a dozen people were killed. While the numbers of protesters were relatively small, there are Arabic social media pages calling for such marches to the fences to occur with greater frequency, especially as September approaches and the Palestinian Authority seeks membership in the United Nations. If tens of thousands of Palestinians were to march, Israel would find itself in great difficulty.

The Obama administration has been trying to balance American support for Israel in the midst of the Arab democracy upheaval, while at the same time supporting the young democracy protesters. But it has been an uphill struggle, Arab analysts said. “It’s become fashionable now to ‘dis’ the Americans,” said Ghaith al-Omari, a former Palestinian peace negotiator who is now a specialist on the region at the American Task Force on Palestine. “The prevalent mood now is to say that the United States is no longer relevant, that the Arab Spring is happening without the help of the United States.”

The economic aid package that Mr. Obama will talk about on Thursday is meant to show democracy protesters, and Arab governments, that the United States stands behind the democracy movement and will reward governments that make reforms. Administration officials announced $1 billion in loan guarantees to Egypt, and $1 billion in debt swaps, along with trade and economic development proposals. Administration officials said an unspecified amount would be channeled to economic development help in Tunisia.

Mr. Obama’s economic aid parallels a package of measures being prepared by the European Union. The union plans to mobilize more than 2 billion euros in investment and development money for Egypt, Tunisia, Libya, and other Middle Eastern countries, drawing on the resources of the European Investment Bank and the European Bank for Reconstruction and Development.

“We’re trying to pull together a kind of strategic approach,” Catherine Ashton, the European Union’s chief foreign policy official, said in an interview on Wednesday. “This is our neighborhood.”

The European aid will focus both on the immediate need for cash and other support — a team of monitors recently went to Tunisia to help officials prepare for elections — as well as longer-term economic development.

Lady Ashton cited a plan by Egypt’s Ministry of Planning to build one million residential houses over 20 years as an example of the projects that the European Union is supporting, because it combines investment, job creation and partnerships with European companies.