Rosenstein's announcement came just ahead of a meeting between Trump and Russian President Vladimir Putin, with whom he has sought warmer relations.
A dozen Russian intelligence officers are facing new US federal indictments alleging they hacked into American computers with the explicit intention of interfering with the 2016 presidential election.
Rosenstein said the announcement of the charges on Friday took place because that was when the special counsel's office had completed its work investigating them and had the ability to present the evidence to a grand jury.
The 12 were members of Russian military intelligence, known as the GRU, and are accused of engaging in a sustained effort to hack the computer networks of Democratic organizations and the Hillary Clinton campaign.
But Trump has frequently wavered on the question of whether Moscow interfered in the 2016 election, which he feels he has not received enough credit for winning.
He also said the Russian defendants infiltrated computers at US state boards of election and secretaries of state, plus software suppliers whose products help election officials verify voter registration data.
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The attacks were a signature feature of Russia's active measures against the United States; embarrassing emails were passed to Wikileaks, which released them publicly.
The groups created the online personas DC Leaks and Guccifer 2.0 used to release the stolen emails, claiming that DC Leaks was a group of American hackers and Guccifer 2.0 was a lone hacker, but Rosenstein said both actually worked for Russian intelligence.
In February this year, Mueller's team unveiled criminal charges against 13 Russians and three Russian companies for interfering in the presidential campaign, using social media and coordinating with low-level Trump campaign activists.
"There is no allegation in this indictment that any American citizen committed a crime", he said at a news conference.
Rosenstein said that while the defendants corresponded with several Americans through the internet, there was "no allegation in the indictment that the Americans knew they were communicating with Russian intelligence officers".