But my observations are as follows.
voltage across R1 is around 3 volts and
voltage across R2 is around 2 volts.
Go back and write the Ohm's Law equations for the two circuit cases with an unknown resistor in parallel with the one being measured, using the two voltages you list. Assume it has the same resistance for each measurement.
Solve each equation, and you will get
different answers for the two solutions, even though one would expect them to be the same.
Why is that?
Using how the two answers differ, make a guess about the actual value of the unknown resistor. Using that value, attempt to calculate (or re-measure the voltages) to derive what should be the actual voltages shown on the meter. You can also solve for the resistance of the meter.