The tweet was the first explicit concession by the president that Robert Mueller, the special counsel for the Russian Federation inquiry, had begun examining Trump's firing of former FBI Director James Comey last month.
With the revelation this week by The Washington Post that Trump was under investigation for possible attempted obstruction of justice, Rosenstein finds himself caught in an awkward pincer - stuck between the wrath of a president who could fire him and questions about his own future role supervising Mueller when he could become a witness in the special counsel's probe.
Jay Sekulow, a lawyer from US President Donald Trump's legal team, denied that Trump was under investigation. Comey also testified Trump had directed him to drop a related FBI investigation into former national security adviser Michael Flynn.
Some of his ire is aimed at Mr Rosenstein and investigative special counsel Robert Mueller, both of whom the president believes are biased against him, associates say.
The White House confirmed that Mueller was among the candidates Trump interviewed to replace Comey.
President Donald Trump shares a laugh with (clockwise from left) Ms.Seema Verma, Administrator of the Centers for Medicare and Medicaid Services, Secretary Tom Price, U.S. Secretary of Health and Human Services, and Vice President Mike Pence on.
"President Trump has started the clock on the Rosenstein firing watch", said Evan Siegfried, a GOP strategist.More news: Ronaldo 'wants to leave' Real Madrid after being accused of tax fraud
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No explanation for the statement was given, but it came just hours after The Washington Post published a story saying Mueller's inquiry is now looking at the finances and business dealings of Jared Kushner, Trump's son-in-law and a key adviser to the president.
The special counsel is looking for evidence to support claims that Trump's associates illegally colluded with Moscow during the president's victorious run for the White House previous year.
Trump has lashed out on Twitter repeatedly, calling the reports of obstruction of justice "phony" and railing against what he called "the single greatest WITCH HUNT in American political history". During an interview with NBC two days later, Trump said he fired Comey because "this Russian Federation thing with Trump and Russian Federation is a made-up story". Trump has expressed increasing dissatisfaction with the Justice Department since Mueller's appointment.
Democrats challenged Rosenstein on whether he would appoint a special prosecutor to look into Russia's election meddling.
Lieu's comments come after Trump and his allies against Mueller's character and possible conflicts of interest in an attempt to discredit him and his investigation.
On May 17 the Department of Justice appointed Mueller as special counsel to head up the Russian Federation investigation.
A Justice Department spokesman told CNBC, "As the Deputy Attorney General has said numerous times, if there comes a point when he needs to recuse, he will".
The panel sent a bipartisan letter this month to White House counsel Don McGahn seeking an answer by this Friday. Pence headed the Trump transition until Inauguration Day. "Nice", Trump tweeted Thursday morning.