The announcement suggests that the effort to wreak electronic havoc across Ukraine is ongoing.
Ukraine is still trying to find its feet after scores or even hundreds of businesses and government agencies were hit by an explosion of data-scrambling software on June 27.
Avakov said in a statement posted to his Facebook page that what he described as the second stage of that malware attack had been timed to hit its peak at 4 PM Ukraine time yesterday.
Avakov said that, like the first attack, yesterday's originated from the Ukrainian tax firm ME Doc.