Saying he came with "a message of friendship and hope and love", Trump told dozens of Muslim leaders that the time had come for "honestly confronting the crisis of extremism".
"This is a battle between barbaric criminals who seek to obliterate human life, and decent people of all religions who seek to protect it. This is a battle between good and evil."
Trump holds talks with Gulf leaders
Trump, who generated controversy with his push to ban many Muslims from entering the United States, described the fight against terrorism as a battle between good and evil rather than a clash of civilisations.
"America is prepared to stand with you in pursuit of shared interests and common security. But nations of the Middle East cannot wait for American power to crush this enemy for them," Trump told leaders of 55 Muslim majority countries representing more than a billion people.
"The nations of the Middle East will have to decide what kind of future they want for themselves, for their countries and frankly for their families and for their children," he said.
Trump praises Sisi, says he hopes to visit Egypt
"It's a choice between two futures and it’s a choice America cannot make for you. A better future is only possible if your nations drive out the terrorists and drive out the extremists.
"Drive them out! Drive them out of your places of worship. Drive them out of your communities. Drive them out of your holy land and drive them out of this earth," he said.
Trump's "America first" philosophy helped him win the 2016 election and has rattled allies who depend on US support for their defence.
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The president, who is struggling to contain a brewing political scandal at home, made clear in his address that Washington would partner with the Middle East but expected more action in return.
"Terrorism has spread across the world. But the path to peace begins right here, on this ancient soil, in this sacred land," he said in Saudi Arabia, the first stop on a nine-day tour that includes Israel, Italy and Belgium.
Trump did not hesitate to single out Iran in his speech.
"From Lebanon to Iraq to Yemen, Iran funds, arms and trains terrorists, militias and other extremist groups that spread destruction and chaos across the region," Trump said.
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"Until the Iranian regime is willing to be a partner for peace, all nations of conscience must work together to isolate it."
Trump received a warm welcome from Arab leaders, who set aside his campaign rhetoric about Muslims and focused on his desire to crack down on Iran's influence in the region, a commitment they found wanting in Obama.
As a candidate, Trump proposed temporarily banning Muslims from entering the United States. In office he ordered temporary bans on people from certain Muslim-majority countries, which have been blocked by courts that ruled they were discriminatory.
Royal welcome
Introducing Trump, Saudi King Salman described their mutual foe Iran as the source of terrorism they must confront together.
"Our responsibility before God and our people and the whole world is to stand united to fight the forces of evil and extremism wherever they are ... The Iranian regime represents the tip of the spear of global terrorism."
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The United States and Gulf Arab countries announced agreement to coordinate efforts against the financing of terrorist groups.
Trump's welcome in the region was put on display during a series of individual meetings with Arab leaders.
He praised Egyptian President Abdel Fattah al Sisi, telling him, "You have done a tremendous job under trying circumstances".
The Obama administration had a difficult relationship with Sisi, who came to power after leading a military coup in 2013 during which hundreds of demonstrators were killed, and has since jailed thousands of opponents.
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Trump promised to schedule a trip to Egypt soon, and he singled out the Egyptian's choice of footwear, a pair of shiny black shoes.
"Love your shoes. Boy, those shoes," he said. To Bahrain's King Hamad bin Isa al Khalifa, Trump declared that the two nations had a lot in common and "there won't be strain with this administration."
The king lauded the relationship and said it had led to "great stability in the region and prosperity".
Bahrain is home to the US fleet in the Middle East.
Trump's Riyadh visit kicks off his first presidential trip abroad, with Saudi Arabia the first stop on a nine-day journey through the Middle East and Europe.
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The speech came as Trump tried to escape the fallout from his May 9 firing of former FBI Director James Comey amid accusations he was trying to stop a federal investigation into his campaign's ties with Russia last year.
The New York Times reported Trump called Comey a "nut job" in a meeting with Russian Foreign Minister Sergei Lavrov last week.
The Washington Post said the probe had reached into the White House to include a Trump adviser, who was not named.
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