Washington (CNN) Attorney General Jeff Sessions is taking responsibility for authorizing Deputy Attorney General Rod Rosenstein to remain in charge of the Russia investigation, and detailed the process by which former FBI Director James Comey was fired.

The comments come amid criticism from Republicans for the Justice Department's decision to keep Rosenstein in charge of the special counsel investigation into Russian election meddling in 2016, and any possible collusion with President Donald Trump's campaign.

Sessions said in an interview released Thursday that he was the one who made the decision to recommend to Trump that he fire Comey, not Rosenstein -- and that therefore Rosenstein isn't disqualified from his role in the Russia investigation.

"That decision ... really fell to me, ultimately, on the Comey matter," Sessions, who recused himself from the Russia investigation, told CNN affiliate Hill.TV's morning show "Rising." "And that's not a disqualifying thing."

South Carolina GOP Sen. Lindsey Graham told CNN last week that he believes Rosenstein is "conflicted" from overseeing special counsel Robert Mueller's work given his role in Comey's firing -- an issue of interest to the Mueller team as it determines whether the President inappropriately sought to interfere with the Russia investigation.

Read More