President Trump said Wednesday that the U.S. recognizes Jerusalem as Israel's capital, a move that puts him at odds with the United Nations and much of the international community. Israeli Prime Minister Benjamin Netanyahu applauded the decision, while Palestinian President Mahmoud Abbas called the U.S. shift "a declaration of withdrawal from the role it has played in the peace process."

What does Mr. Trump's announcement mean for the immediate prospects of the Middle East peace process? It depends who you ask, CBS News' Seth Doane reports.

"On the Israeli side, you have people, many who were overjoyed," Doane said. "Israeli Prime Minister Benjamin Netanyahu came out right after with a statement and said that in the great 3,000-year history of the Jewish people's connection and belief that Jerusalem was their capital, this was a significant day."

But on the other hand, Palestinians felt the opposite. Doane said he asked one senior Palestinian official about Mr. Trump's reputation of being a deal maker, and "she laughed at us ... She said 'the ABCs of deal-making are not to give everything to one side.' And this is how this is being viewed by Palestinians."

Mr. Trump's recognition of Jerusalem as the capital of Israel rejects the policy of previous administrations and the recommendations of his secretaries of state and defense, CBS News' Major Garrett reports.

But administration officials could point to no evidence this symbolically important shift in U.S. policy will accelerate peace talks. Mr. Trump's son-in-law Jared Kushner is leading that White House effort and has yet to formulate a plan, according to Garrett.

Holly Williams, a CBS News correspondent based in Istanbul, said Muslims around the world view this news as a "slap in the face because so many of them support Palestinian dreams of statehood."

"Here in the Middle East, many, many people have somehow come to believe that the U.S. is waging a war against Islam and against Muslims. And they will see this as more evidence of that," Williams said.

CBS News spoke to King Abdullah of Jordan, a very important U.S. ally, who met with Turkish President Recep Tayyip Erdogan in Istanbul. Abdullah told CBS News "this move could fuel extremism and undermine the war against terrorism," Williams said.

"But the criticism isn't just coming from Muslims. European leaders and China have both voiced their concerns," Williams said. "And today, even the pope spoke out, saying that he prayed that wisdom and prudence would prevail."

But Williams noted that leaders feel there is not much their governments can do. "But next time the U.S. wants cooperation from Middle Eastern governments in this very important of the world -- because of oil, because of its location, because of terrorism -- this won't help," Williams said.

Doane, who is in Jerusalem, said there are already protests in Gaza. Several Palestinian groups have called for a "Day of Rage" protests on Friday, Doane reported.

"Just after the president's speech, after that announcement tonight, we had a mosque come out and say that this announcement opens the gates of hell," Doane said.