With AC, I prefer the humdity to run around 55 - 60%.
Do you have an idea as to the source of the moisture?
Is this an inside or outside wall?
Is this a ground level room on a slab foundation?
Are there visible signs of moisture on or at the base of the wall?
Is this a window AC? If so, is the condensation draining properly?
If your AC unit is larger than necessary for the job, it will cool the room down to the temperature setting before completing dehumidification.
How high does the outside humidity run in your area?

Thanks for your help. Yes, I had someone check and the AC was tilted incorrectly. Humidity levels have been lower. Humidity is better; however, still a bit higher in room with AC on than off. I think there may be an additional problem of moisture in wall next to AC. I am wondering if AC can be making possible moisture worse?

If the A/C was tilted inward, it's probable the condensate that went into the wall. If there were no puddles on the floor it went someplace.
Take tha A/C out and check the sill of the window for wetness, holes or peeling paint. If water got into the wall you need to open it up under the A/C to dry it out. If the whole bay is wet, open one bay to each side and keep going until you get bays that are partially dry.
Replace any wet insulation after treating for any mold.
I'd also check the floor below to see if the ceiling is stained or the paint is peeling.
Ron

I had the AC repositioned; however, I am concerned about the moisture in the wall next to AC. There was slight bulge in that wall with what appeared to be plaster bulging out. Landlord had someone plaster over it and they are coming back to paint. They are also going to do outside pointing on bricks. Someone told me that bulge could definitely be indicative of moisture inside wall. I have friends who say bulge was from AC and others think from exterior. Landlord refuses to check for moisture in wall so I am trying to persue this myself and get someone to check. I am trying to secure used non invasive moisture meter. Am I going in right direction? Thanks.