It is not inconsistent per se since there are more than just one channels through which price level and interest rate interact.
For example, in a IS-LM AS-AD, model when central bank decreases interest rate, initially LM curve shifts down, which leads to higher price level (so they move opposite to each other) and lower output (lower output is caused by movement along IS curve - e.g. people consuming less due to higher interest rate). However, as a result of higher price level people now demand higher real money balances which shifts LM curve back up and interest rate increases (here price level moves in same direction as interest rate). The economy ends up with the previous rate of interest and much larger price level (draw horizontal line from A'').
This is probably best understood graphically, the graph below (from Blanchard et al Macroeconomics 2nd ed pp 171) visualizes what I have written above. Please ignore in the graph LM'', that part shows what would happen if price level was fixed which is not relevant for your question or this answer.
As you can see from the graph, both statements are completely consistent with each other. Economy is an endogenous and highly complex system, often change in one variable will have different effect in short/medium/long run, and even in the same time span one variable can trigger through various channels effects that counteract each other. This is not sign of inconsistency, economics is not like physics where many forces are exogenous and less complex.
