A300 pilot reported a Master Caution and a Main Deck Door Not Closed ECAM Message in cruise. The flight crew ran the check lists and QRH. Cabin Altitude was also increasing so the flight crew requested priority handling and immediately descended. Cabin Altitude stabilized at 10;00 feet; so the flight crew continued to land at destination airport.

Narrative

After we had been cruising for a while we got a master caution and the main deck door not closed ECAM message. We followed the ECAM checklist which had us check the cabin rate to see if it was normal. The cabin rate was indicating a 500-600 foot climb with the cabin altitude was also increasing. This is for sure not normal as we had been in level flight for a good while. We then followed the rest of the ECAM and selected 10;000 ft. in the Landing elevation window and called ATC to [request priority handling] and informed them that we had a door indication with a rising cabin altitude which required a descent to 10;000. In the descent we were still showing the cabin rate climbing until around 25;000 ft. or so but the door message stayed on all the way to landing. During the descent we started talking about diverting to ZZZ which was the closest airport but as we leveled at 10;000 the cabin was stabilized. The QRH states that if the cabin can be stabilized that you can continue normal flight so we felt it safe to continue 90 miles to ZZZ1. To air on the side of caution we didn't cancel our [priority handling] at that time and landed in ZZZ1 where we had Crash Fire Rescue verify that our door wasn't opened and that nothing was hanging or protruding from the aircraft. After that was verified we continued to the Ramp where we had maintenance come on board and open the cargo door.