"The stolen vehicles would have been used by a range of Kiwis who were returning to work as the country moved to level 2," he said.
"At Jucy, we have about two-and-a-half thousand vehicles across New Zealand - cars and campervans, so it's a significant number that has been taken from us."
At least 35 of the stolen vehicles had been recovered by police as of Monday afternoon, he said.
Staff were checking their stock of rentals across the company's multiple sites so see if any more were missing.
Alpe said he believed the theft occurred on Saturday, Anzac Day.
"There's a full police investigation at this stage, as well as an internal one to understand how many vehicles were taken, but it's at least 60," he said.
Inspector Matt Srhoj, Counties Manukau West Area Commander, earlier told the Herald it was believed around 100 vehicles, registered to Jucy Rentals, were stolen from the company's Māngere yard.
"We're a big operation, but it's just devastating right now, when tourism's just been decimated," Alpe said.
"To have to go through this as well is just horrific."
Police had increased patrols in the area and inquiries were made over the weekend, a spokesman said.
"The investigation is ongoing into the theft and police are continuing our inquiries to establish exactly when and how the thefts took place."
The stolen vehicles were Holden Captivas, Mazda 3s or Suzuki Swifts and were plain without branding, making them not easily identifiable as Jucy rental vehicles, Srhoj said.