How/Whether to correct a wrong paper published in a prestigious journal There are several publications which I was advised to read by my supervisor, and work on during my master thesis. At some point I tried re-deriving the presented statements formally, and found that there are major mistakes that make the publications wrong in a very large part. I have had several people re-derive the same results and arrive at the same conclusions as me since. The issue seems to have started with two publications which used informal (and wrong) logic to argue about the correctness of their main statements. This has been cited over a period of almost a decade and various formalizations and analyses have been done on top of that (including PhD theses) - most of which will turn out to be irrelevant if the results on which those are based are shown to be wrong. A lot of the follow up publications have been published in some of the most prestigious journals in the field.

I tried talking with my supervisor (which is a co-author in some of those) about the issue. Initially he wanted me to find cases in which the statements in the publications hold, however it turns out there are no such cases. Since I notified him of this fact, he has been dodging the issue, even when I suggested that we should at least contact the authors.

How should I proceed with this issue? The publications in question keep being cited and have resulted in even more wrong publications in the last years, as well as wrong conclusions in mainly correct publications.
It is hard to tell whether you are on firm or shaky ground. If the ground is firm, probably the best way to approach it is to write a paper yourselves with correct results and see if the same journal will publish it. 

But, the ground may be shaky for the following reasons. 

In mathematics, a failed proof doesn't leave the result false, just unproven. It gives no evidence for the validity of the claim. A counterexample, on the other hand, leaves the result certainly false. So, it may be that, while an argument fails to deliver, the overall result is still correct, just not provably so. 

But a result that is (if true) contradictory to the original, then the original must be false. This is actually stronger than a counterexample, since a counterexample only shows that a general statement is false, but might leave some specialization of it true, provided that the specialization excludes the counterexample. 

However, in this case you say that your analysis leads to different results. If those results are contradictory to the original claims, and if your reasoning is correct, then you may have the basis of a paper. 

However (again), if your results aren't, in fact, contradictory, then your advisor is giving good advice that you explore the intersection of what it is that the original paper claims and what you claim from your analysis. This might also give you the basis for a good paper, leaving some of the original claims win place, but improving on them. 

I suspect that the situation is complex enough that a simple letter to the editor of the journal, pointing out the error, isn't going to be sufficiently compelling for anyone to take action. If the journal in which you find the original is reputable, then many people have missed the errors, implying a certain subtlety. This leads me to suggest that a full paper laying out the situation is more appropriate. 

And even if this invalidates some early work of your advisor, he is at an advantage in being part of the process that corrects it.