The promotion was announced yesterday and will be available starting next month until February 13, in Canada and United States.
Customers who trade in their iPhones could receive up to USD 400 cash back depending on the model and condition of their trade-in, plus a USD 150 gift card.
This marks the first time that BlackBerry has gone head-to-head with Apple since the Canadian firm launched a turnaround plan last year aimed at stemming massive losses.
The Passport was launched in September.
Named for its approximate size to the travel document, the phone was designed to win back key corporate users after BlackBerry was effectively knocked out of the highly competitive consumer smartphone market dominated by Apple and Samsung.
Investors seemed pleased, pushing up the Waterloo, Ontario-based company's share price slightly in morning trading.
But analysts were more skeptical. Carl Simard of Medici called it a very "desperate move."
In September, BlackBerry reported it narrowed its loss in the latest quarter, and expressed optimism that its major restructuring and new business-friendly devices would help fuel a turnaround.
For the three months ended August 30, BlackBerry posted a loss of USD 207 million on USD 916 billion in revenues largely split between sales of services and software and more than two million smartphones.
The Canadian manufacturer pioneered the smartphone market but has struggled to keep up with competitors in recent years.
Last year, the company introduced the BlackBerry 10 operating system and new smartphones in an effort to regain ground lost to rivals such as Apple and others using the Google Android operating system.