My Wirlpool Imperial Seventy Washing machine keeps filling with water and when it reaches the desired level I set it at, it empties 2/3 of the water and the refills itself to the desired level and repeats the action all over again. I have tried all of the settings and water levels and it does the same thing again.

Is the drain hose just hanging in the drain pipe or is the connection sealed?

The drain hose fits snuggly into the drain pipe. The washing machine fills up, Acts as if it is going to start agitating and then the pump empties the water about 2/3's and refills through the cycle (regular, heavy duty, perm press, delicate) until it gets to the spin cycle. Then it starts spinning and rinsing the clothes as if it agitated them and completes the cycle.

Does the pump pump the water out or does it just drain out? Just to see what happens, fit the drain hose in the drain pipe loosely so that it can get some air into the drain pipe. If you have a laundry sink nearby put the drain hose in the sink.

I put the drain hose in the sink and started the washing machine and it did the same thing, It filled up stopped the pumped the water 2/3 empty then started to refil it again. I also found out that it does agitate on the delicate cycle. It also agitates on the gentle knits cycle

Im afraid you will have to call an appliance repairman. Sounds like you have a defective timer.

The reason for questions about the drain was because if the drain hose is sealed in the pipe and the venting of the plumbing is not correct, water flowing out of the drain can suck water out of the washer.

You said the washer drain pump is coming on when the washer should be agitating. That makes me think that something is wrong with the timer mechanism.