A C680 flight crew experienced a cabin pressurization control problem during climbout. The crew decided to return to the departure airport when unable to resolve the pressurization issue.

Narrative

Somewhere between 16000 and 18000 feet on the climb out; the Amber Cabin Altitude Message came on. I instructed my partner to grab the check list. As he was turning to the appropriate page; the CAS Message turned to Red. Shortly after that; I informed ATC that we needed lower or to level off. They gave us an altitude and we were at 16000 shortly. In the meantime; I instructed my partner to put on his mask. He did so and then I gave him control of the aircraft. Because we were at 16000 feet and descending; I did not feel it was needed to do an emergency descent. I informed the passengers of the situation and told them that I would be manually dropping the mask and to use them if required. I then put on my mask and we completed the check list and continued down. I don't believe the cabin altitude ever exceeded approximately 12000 feet. When we got to 6000 feet; I called the company to coordinate a landing location and recovery plan. On the descent; the Amber Left and Right Wing Anti Ice Over Heat CAS message came on. We ran the check list and eventually returned to our departure airport with no further events. ATC was very helpful. No emergency was declared.