Samsung recalled 2.5 million phones last week after reports emerged of the device exploding during or after charging.
And airline passengers were warned by US authorities not to switch on or charge the phones while on board.
The South Korean company said it would replace all devices that were handed in from 19 September.
A statement by Samsung, the world’s biggest mobile phone maker, said “our customers’ safety is an absolute priority”.
“Until a replacement device is provided, Samsung asks all customers with a Galaxy Note 7 smartphone to power down your device and return it to its place of purchase at your earliest opportunity,” the statement added.
Earlier on Saturday, aviation authorities in the United Arab Emirates banned use of the devices on the Emirates and Etihad airlines.
The US Federal Aviation Administration (FAA) also advised against packing the phones into any checked-in luggage.
Samsung recalled the phone last week after reports emerged of the device exploding during or after charging.
US TV channel Fox 10 reported claims that a faulty Galaxy Note 7 had set fire to a family’s Jeep.
Samsung has said that battery problems were behind the phones catching fire, but that it was difficult to work out which phones were affected among those sold.
The phone was launched last month and has been otherwise generally well-received by consumers and critics.