Brand was only sworn-in on May 22. Rosenstein himself was confirmed by the US Senate on April 25.
On May 9, he wrote a memorandum outlining reasons why President Donald Trump should fire then-FBI Director James Comey.
Trump fired Comey on May 9, initially citing Rosenstein's memorandum, but later telling NBC News anchor Lester Holt that he always planned to fire Comey. Rosenstein told the Senate on May 17 that he knew Comey would be fired before he wrote the memo.
Trump claimed on Friday that he was being investigated "for firing the FBI Director by the man who told me to fire the FBI Director!"
Comey's termination prompted a deeper investigation into whether Trump obstructed justice in the Russia investigation, and Comey told the Senate Intelligence Committee last week that Trump asked him in January to drop the FBI probe into former National Security Advisor Michael Flynn's communications with Russian officials.
US Attorney General Jeff Sessions previously recused himself from the Russia probe as he was part of the Trump's election campaign and didn't tell during his confirmation at the US Senate that he met Russian Ambassador to the US Kislyak.
Russia has repeatedly denied meddling in the 2016 US presidential election, insisting that it does not meddle in the affairs of other countries.