A customer, right, looks at merchandise with an employee at a Sprint Corp. store in Palo Alto, California.

Preorders of this year's new iPhone on Sprint were nearly five times higher than last year's iPhone 6s launch, CEO Marcelo Claure said Tuesday.

"The iPhone 7 for us has been a smashing success," Claure said CNBC's "Squawk on the Street."

Claure's comments came after Sprint announced last week that in the first three days of the preorder period, customers were placing orders for the iPhone 7 at a rate more than 375 percent higher compared to the same period during launch of the iPhone 6s last year.