Government shutdown updates: Leavitt says Trump exploring cutting aid to Portland

Near the end of his remarks, President Donald Trump called on Hamas to accept what he called his "extremely fair" proposal.

"Everybody who wants to see an end to the violence and destruction should be united in calling for Hamas to accept the extremely fair proposal so that we can end the war and get us back our hostages right now and have everlasting peace," he said.

Among the new details in Trump's plan, it requires Hamas to disarm gradually and requires the IDF to gradually withdraw but leaves them in control of the Philadelphi corridor and the established buffer zone. It also leaves a role for the Palestinian Authority -- after reforms -- to take part in running Gaza and leaves the option open for future Israeli-Palestinian negotiations for Palestinian statehood.

President Donald Trump spoke about the teleprompter issue that wasn't working when he spoke during his United Nations visit last week.

"They're introducing me but there's nothing on my teleprompter," Trump said on Monday.

He said since the teleprompter wasn't working, his speech was "better in certain ways" as it was "more of a speech from my heart."

President Donald Trump referred to his plan as an opportunity for Palestinians to "take responsibility for their destiny," and said the U.S. will "be there with you in terms of helping with security."

"There are many Palestinians who wish to live in peace," he said. "I challenge the Palestinians to take responsibility for their destiny, because that's what we're giving them. We're giving them responsibility for their destiny, fully condemn and prohibit terrorism and earn their way to a brighter future."

Trump said if the Palestinian Authority does not complete the reforms laid out in his vision for peace, "they'll have only themselves to blame."

"What the future holds for the Palestinians no one really knows, but the plan that we put forward today is focused on ending the war immediately, getting all of our hostages back, getting everything back ... and creating conditions for durable Israeli security and Palestinian success," he said.

"Israeli security is going to be involved. We're going to help you. We'll be there with you, in terms of helping with security. We want to make sure it works," Trump continued.

President Donald Trump said that he will head a new international oversight body called the Board of Peace that will be responsible for "recruiting and training a new government that will be made up of Palestinians."

The board will also include leaders from other "distinguished" world leaders, including former U.K. Prime Minister Tony Blair, Trump said.

Trump said that Hamas and "other terrorist factions will play no role in the board."