Prince Alwaleed bin Talal had reacted to the Republican presidential frontrunner's proposal earlier this week that all Muslims should be temporarily barred from entering the United States.
"Dopey Prince Alwaleed Talal wants to control our US politicians with daddy's money. Can't do it when I get elected," Trump wrote on Twitter, in the same typically confrontational fashion that has been the earmark of his bombastic presidential campaign.
It came after Alwaleed, a devout but moderate Muslim, took exception to what his office called Trump's "anti-Islam statement."
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"You are a disgrace not only to the GOP but to all America," Alwaleed had tweeted to Trump, referring to the Republican Party.
"Withdraw from the US presidential race as you will never win."
Alwaleed is an unusually outspoken member of the Saudi royal family who chairs Kingdom Holding Co. The diversified firm's interests include US-banking giant Citigroup.
Trump has been lambasted both in the US and abroad for his Muslim plan, which followed a shooting rampage by a Muslim couple in San Bernardino, California, which left 14 dead.