Yes, a few of the car rental companies in Iceland will accept a debit for the local security deposit. To display only those suppliers that will accept debit card, tick the debit card box selection filter on the car quotes results page
The card is required for the local security deposit that will be refunded on the safe return of the rental vehicle.

Blue Car Rental Iceland : The renter, or someone travelling with the renter, also needs to submit a credit card on arrival when he picks up the vehicle. We require the renters to submit a credit card, but if you only have a debit card, Blue Car Rental will accept debit cards with a 16-digit number on the front.

Zezgo
Saga
Faircar

For the latest up-to-date list, please use the filter on left-hand side to select car hire companies that will accept a debit card for the local security deposit, in case the list changes or additional suppliers change their conditions of rental.