It wasn't clear whether the president was basing his tweet on direct knowledge that he is under investigation, or on reports this week that special counsel Robert Mueller is examining whether the president obstructed justice by firing former FBI director James Comey last month amid the ongoing Russian Federation investigation. In March, Sessions recused himself from decision-making in the investigation.
Trump's tweets came after the top lawyer for his transition team warned the organization's officials to preserve all records and other materials related to the Russian Federation probe. If he fires Rosenstein, Brand would lead the department.
That's because the deputy attorney general could become a potential witness in the investigation.
Depending on how events play out, the Justice Department could face a crisis not seen since the so-called Saturday Night Massacre when President Richard Nixon's attorney general and deputy attorney general resigned after being ordered to fire the independent special prosecutor overseeing the Watergate investigation, said Jeffrey Cramer, a former federal prosecutor.
Rosenstein's comments weren't attached to any particular story, though the Washington Post had just reported that Mueller's probe had expanded and investigators were looking into the president's son-in-law Jared Kushner's business dealings.More news: 3 share lead after 2 rounds at St Jude Classic
Robert Mueller, the special counsel named by the department to investigate the Russian Federation matter, is now examining whether Trump or others sought to obstruct the probe, a person familiar with the inquiry said on Thursday.
Rosenstein could eventually be questioned by Mueller about his memo on Comey and what motivated Trump to ask him to write it.
Trump said Friday that he was under investigation over his firing of Comey, saying he was being investigated "by the man who told me to fire the FBI Director". The tweet comes amid reports that Trump may want to fire Mueller, which only Rosenstein is legally able to do.
Earlier this month, Rosenstein told The Associated Press that "if anything that I did winds up being relevant to his investigation then, as Director Mueller and I discussed, if there's a need from me to recuse, I will".
The Justice Department on Friday said any such of consideration of recusal was premature. She left the Justice Department in 2007 and spent three years at WilmerHale, a law firm that typically represents corporate interests.
She also echoed concern that the president will try to fire Mueller and Rosenstein. He's increasingly focused his anger at both Rosenstein and Mueller, according to advisers and confidants, viewing the two as part of a biased effort to undermine his presidency.
In another indication of the seriousness of the probe, Michael Cohen, a personal attorney to Trump, said he has retained attorney Stephen Ryan, a former assistant United States attorney, to represent him in the ongoing probes. Trump named Boente as acting attorney general in late January after firing Sally Yates for refusing to defend his original travel ban.