The focus on Rosenstein sharpened Friday because the President attacked the deputy attorney general in a tweet, blaming him for what he terms a "witch hunt".
Rosenstein's statement appeared just hours after The Washington Post reported Mueller is looking into the business dealings of Jared Kushner, President Trump's adviser and son-in-law, based on unnamed American sources. At the time, Trump said he was going to fire Comey regardless of Rosenstein's memo and that Russian Federation was on my mind. The Washington Post reported this week that Mueller is investigating whether Trump attempted to obstruct justice when he suggested Comey drop an FBI investigation into Michael Flynn, Trump's former national security adviser, as well as when he fired Comey.
Starr is best known for his work investigating former President Bill Clinton in the 1990s.
The President complained the probe was unfair and wondered why his defeated Democratic opponent was not getting the same scrutiny. But he had said last week he felt vindicated by Comey's testimony on June 8 that he was not the subject of investigation while Comey was heading the agency.
Several investigations could pose trouble for Trump. A spokesman for Trump's personal attorney had strong words in response to the news.
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.
According to associates, Trump believes both Deputy Attorney General Rod Rosenstein, who was brought in to oversee the inquiry after Jeff Sessions and Robert Mueller, the special investigator, are biased against him. That report was attributed to unnamed USA officials.
As time passed and public suspicion grew in the Russian Federation probe, particularly because of Trump's firing of Comey, Rosenstein responded with the appointment of Mueller.
A memorandum penned by Rosenstein was cited by the Trump White House as the inspiration for the May ouster of James Comey, then-director of the Federal Bureau of Investigation.
"Why is that Hillary Clintons family and Dems dealings with Russian Federation are not looked at, but my non-dealings are?" he asked at one point.
Moscow has denied any interference.
However, since the table is turned now, Trump is feeling like "he is the victim of a conspiracy aimed at discrediting his presidency and ultimately ending his tenure of the White House".
After Trump's tweet Friday morning, a person close to the president's legal team told NPR's Scott Horsley that the tweet referred to the Wednesday Washington Post report regarding possible obstruction of justice.
The Senate Intelligence Committee is holding a public hearing next week to gather more information on Russia's interference in last year's elections. He is reportedly being investigated over whether he tried to obstruct law enforcement investigations into his associates or into the Russian Federation matter.