President Donald Trump said there was a "very, very good chance" that he could bring the Palestinians and Israelis together to achieve peace during a Wednesday press conference alongside Palestinian President Mahmoud Abbas.

"I will do whatever is necessary to facilitate the agreement, to mediate, to arbitrate, anything they'd like to do -- but I'd love to be a mediator, or an arbitrator or a facilitator, and we will get this done," Mr. Trump said.

Mr. Trump also warned Abbas that the Palestinians will have to take certain steps to bring the Israelis on board: "There can be no lasting peace unless the Palestinian leaders speak in a unified voice against incitement to violence and hate, there's such hatred, but hopefully there won't be such hatred for very long."

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Abbas gave Mr. Trump credit for trying, saying "you have the determination to be successful" and that they could be "historic partners."

Palestinian President Mahmoud Abbas delivers a statement accompanied by U.S. President Donald Trump during a visit to the White House in Washington D.C., U.S., May 3, 2017. Reuters/Carlos Barria

Abbas also called for a Palestinian state with East Jerusalem as its capital -- a day after Vice President Mike Pence said that the U.S. was giving serious consideration to recognizing Jerusalem, not Tel Aviv, as the capital of Israel. Abbas also detailed his view on what a two-state solution to the issue would look like, including recognition of the Palestinian state by Israel.

However, Mr. Trump mostly spoke in generalities about peace talks. He noted that he had spoken to Israeli Prime Minister Bibi Netanyahu about re-energizing talks, but remained uncommitted to a two-state solution.

"Over the course of my lifetime, I've always heard that perhaps the toughest deal to make is the deal between the Israelis and the Palestinians -- let's see if we can prove them wrong, ok?" Mr. Trump said.

CBS News' Margaret Brennan contributed to this report