"Drive them out of this earth," he told regional leaders in Riyadh as part of his first official trip abroad.
Mr Trump singled out Iran for being responsible for instability in the region, saying it should be "isolated".
His speech is seen as a reset with Muslims after his campaign rhetoric stirred concerns in the Islamic world.
Mr Trump had previously suggested he would be open to creating a database of all the Muslims in the US, also called for Muslims to be temporarily banned from entering the US over security concerns.
'Good vs evil'
Speaking in the Saudi capital, Mr Trump called this a "new chapter", saying he was not there to "lecture" the countries or impose America's way of life.
The fight against extremism, he added, was not a battle between different faiths: "This is a battle between good and evil".
But, he said, the countries could not wait for "America power" to act.
"We can only overcome this evil if the forces of good are united and strong, and if everyone in this room does their fair share and fulfils their part of the burden."

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Saudi are the founders and funders of terrorist