He also warned against those who would finance terrorism, saying: "We will never be lenient in trying anyone who finances terrorism, in any way or means, to the full force of the law."
The address came at a gathering of more than 50 majority-Muslim countries at the Arab summit in Riyadh. Notably, Syria and Iran were absent from the talks.
The accusation that Iran is exporting extremism to the world demonstrated the regional and sectarian tensions that divide Sunni Saudi Arabia and Shia Iran.
The Independent’s Middle East correspondent Robert Fisk argued that Mr Trump’s trip to the region would inflame an already electric political climate.
In the televised address, the king told audiences across the world that “we did not know terrorism and extremism until the Khomeini revolution reared its head”, referring to the 1979 Iranian revolution.
Saudi Arabia and the US recently announced a $110bn (£84.4bn) arms deal – the largest in the history of the country.
Speaking after the king, Donald Trump echoed his sentiments, and blamed Iran for providing Syria with "safe harbour, financial backing and the social standing needed for recruitment [of terrorists]".
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