High value resistors in AD8622 differantial mode amplifier configuration

I'm applying two sinusoidal signals to the inputs of a AD8622 which is configured in differantial amplifier mode. The applied signals swings from -1.65V to +1.65V @1KHz. The applied signals have a phase difference of 180 degrees. I'm using amplifier to measure the difference of the input signals. The amplifier has a gain of 3 and has dual supply of +-12V. When I use resistors below 1M or around to configure the opamp, there seems no problem at the output. But when I increase the value of the resistors to say 5M or 10M, then the output signal has a component oscillates within the original signal like @100KHz with a half or one third of the amplitude of the original signal. I need to use high value resistors and cannot use instrumentation amplifier configuration due to space constraints. What may be the problem and what can I do?