The summit will be one of three forums held during a visit by Trump, who is making Saudi Arabia his first overseas stop since assuming office in January.
Trump has frequently been accused of fuelling Islamophobia but aides described his decision to visit Saudi Arabia as an effort to reset relations with the Muslim world.
Along with the six-nation Gulf Cooperation Council (GCC), at least 18 other Muslim nations have been invited to the summit, including Turkey, Azerbaijan, Niger and Indonesia, which has the world's largest Muslim population.
Saudi Arabia's regional rival Iran is not invited.
Salman told a cabinet meeting in the Red Sea city of Jeddah that the meeting "comes in light of the challenges and sensitive situations that the world is going through".
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According to the official Saudi Press Agency, "he expressed his hope that this historic summit will establish a new partnership in the face of extremism and terrorism and spreading the values of tolerance and coexistence" while enhancing security.
Trump is to also hold a bilateral summit with Saudi Arabia and talks with the GCC on Saturday.
Washington and Riyadh have a decades-old relationship based on the exchange of American security for Saudi oil.
But US ties with Riyadh and its Gulf neighbours became increasingly frayed during the administration of president Barack Obama.
Saudi leaders felt Obama was reluctant to get involved in the civil war in Syria and was tilting toward Shiite-dominated Iran.
The Saudis have found a more favourable ear in Washington under Trump, who has denounced Iran's "harmful influence" in the Middle East.