Sources told ABC that Rosenstein told Associate Attorney General Rachel Brand that she would have to assume those responsibilities if he recused himself. Rosenstein appointed special counsel Robert Mueller to investigate alleged Russian meddling in the 2016 US election, and has told lawmakers he would only fire him with good cause.
US President Donald Trump has confirmed he's being investigated for his role in firing Federal Bureau of Investigation director James Comey, calling the probe a "witch hunt".
Rosenstein wrote a three-page memo on May 9 criticizing Comey for his handling of the investigation into former Secretary of State Hillary Clinton's use of a private server while in office. Last month, Rosenstein sent a memo to Trump raising concerns over FBI Director James Comey - concerns the White House then cited as a central reason for Comey's firing.
If Mueller strays from the straight and narrow, Rosenstein should not hesitate to remove him and name someone else to serve as special counsel. Trump fired Comey on May 9. A spokesman for Kasowitz did not immediately respond to a request for clarification.
The special counsel overseeing the investigation into Russia's role in the 2016 election is interviewing senior intelligence officials to determine whether President Trump attempted to obstruct justice, officials said.
The order by the general counsel for the transition team casts a wide net on documents that could shed light on ties between Trump's presidential campaign and representatives of Russia's government.
It was not clear what prompted the statement, although it came hours after The Washington Post reported that the business dealings of Trump's son-in-law, Jared Kushner, are being examined as part of Mueller's investigation.
The memo identifies several Trump officials and advisers whose records are of particular interest in the probe.