In an apparent policy shift, President Obama on Thursday invited Hamas -- a designated terror organization -- to "play a role" in the future of the Palestinian people.

During his speech to the Muslim world in Cairo on Thursday, the U.S. president bluntly recognized the group, which has called for the destruction of Israel, in a two-sentence passage that was part of a broader discussion about the terms for peace between the Israelis and the Palestinians. 

"Hamas does have support among some Palestinians, but they also have to recognize they have responsibilities. To play a role in fulfilling Palestinian aspirations, to unify the Palestinian people, Hamas must put an end to violence, recognize past agreements, recognize Israel's right to exist," Obama said.

The president then called on Israel to end settlement construction and for both sides to embrace a two-state solution. He reiterated that the U.S. bond with Israel is "unbreakable."

Some observers said they were struck by the firm tone Obama took with both sides in addressing the generations-old conflict and particularly with his recognition of Hamas, which may signal to the group that it is seen as an inevitable part of the Palestinian future.

"That is a major shift in Middle East policy and it's not good," said Marc Thiessen, former speechwriter for former President George W. Bush, who sought to isolate Hamas.

"Israel has reached out to the Muslim world by giving Gaza back and they have even talked about a Palestinian state. But all of these entities, Hamas, Hezbollah and others, have said Israel's right to exist should not be guaranteed," said Rep. Dan Burton, R-Ind., ranking Republican on the House Foreign Affairs Subcommittee on the Middle East and South Asia.

The three "responsibilities" Obama mentioned  -- an end to violence, recognition of past agreements and of Israel's right to exist -- have been part of U.S. policy toward Hamas for years. But those responsibilities are often stated as conditions for engagement with Hamas -- not for implied Western support of Hamas governance. 

Bruce Riedel, a foreign policy fellow with the Brookings Institution and former Middle East adviser to several U.S. presidents, said Obama -- ever the pragmatist -- was merely trying to steer an undeniable force in Palestinian life and politics into the mainstream.

"I think he's challenging them. ... He's saying if you want to lead your people forward, here's what you need to do," he said. "The reality is Hamas now controls Gaza, more than 1 million people. It can't be ignored."

Currently, the Fatah government of Mahmoud Abbas is in charge of the Palestinian Authority in the West Bank. Hamas controls the Gaza Strip, which Israel vacated in 2005. 

Fatah and Hamas broke ties from a coalition government two years ago when Hamas won a majority of votes in parliamentary elections, but could not control key ministries and maintain Western support because of its widespread designation as a terror group.

One Hamas official Mahmoud Ramahi offered qualified praise for the speech.

"I have followed the speech closely. There are many positive points," Ramahi is quoted saying in the Jerusalem Post. "There is a difference between his policy and Bush's policy. I see a change in the U.S. foreign policy discourse." 

Other Palestinian leaders also praised the tone Obama took in his address. 

"This speech touched me because it's the first time an American president saw the human face of the Palestinians," Mustafa Barghouthi, a member of the Palestinian Legislative Council, said in a statement. 

As for Obama's statements on Israeli settlements and the two-state solution, Riedel said they were tough, but necessary.

"It was about as direct and forceful as you could have gotten... he didn't pull any punches with either side," he said, noting that Obama's also forcefully condemned Holocaust deniers, a message likely aimed at Iranian President Mahmoud Ahmadinejad, and those who call for the destruction of Israel. But he said the speech is sure to cause a backlash in Israel.

"The Israelis are not going to like some of what they heard, especially about settlements," he said.

In the days leading up to his address, the president's prior call for Israel to abandon all settlement construction drew criticism in the Jewish state, and had been rebuffed by Prime Minister Benjamin Netanyahu.

Netanyahu's issued a statement after the speech praising the U.S. president in broad terms.

"The government of Israel expresses hope that President Obama's important speech will lead to a new period of reconciliation between the Arab and Muslim world, and Israel," the statement said. 

"Israel is obligated to peace and will do as much as possible to help expand the circle of peace, while taking into consideration our national interests, the foremost of which is security," it concluded.

But Israeli media reported Thursday that settler leaders were frustrated by Obama's address.

Habayit Hayehudi chairman Daniel Hershkowitz was quoted saying Obama presented a "fabricated history" and ignored those Palestinians who have not renounced terror.

"The government of Israel is not America's lackey. The relations with the Americans are based on friendship and not submission, and therefore Israel must tell Obama that stopping natural growth in the settlements is a red line," he said, according to the Jerusalem Post.

Obama's speech also exposed divides among Israel's lawmakers over the settlement and statehood issues. Other politicians welcomed Obama's tough talk, and said it proved Netanyahu represents narrow interests by opposing elements of that roadmap to peace.

Meanwhile, Palestinian news outlet Ma'an News Agency reported that Hamas invited Obama to visit the Gaza Strip in a letter -- which anti-war group CodePink planned to deliver Thursday.

In the letter, Hamas urged Obama to visit the territory to "witness the results of the Israeli war," referring to the offensive launched by Israel in late December in response to a barrage of rocket fire from the Gaza Strip.

"Such a visit will put the United States in a higher position in the view of the entire world in order to solve the conflict," the letter said. 

Click here to read more about Obama's overseas trip.