If you impugn something such as someone's motives or integrity, you imply that they are not entirely honest or honourable. The Secretary's letter questions my veracity and impugns my motives. to express doubts about someone's honesty, courage, ability etc (impugnare, from pugnare )
To attack by words or arguments; to contradict; to assail; to call in question; to make insinuations against; to gainsay; to oppose