I think it is undecidable, let L is RE language that can be accepted by TM. Let W belongs to L and if we input this to TM, it will will definately tell, the given W is present in language. let W be a string which is not in L. If we give this to TM, it will complete all its steps but it is not guaranteed that TM will tell given W is not in L. Hence not decidable.
TM halting problem which is undecidable can be converted to the above problem, so by reducibility property the above problem is undecidable.
Correct me If iam wrong.