"I think it would be very difficult... for anybody to find somebody better qualified for this job," Rosenstein said. "Director Mueller has, throughout his lifetime, been a dedicated and respected and heroic public servant."
Mueller is a Republican who was appointed as special counsel by a Trump nominee.
In August, FBI investigator Peter Strzok was removed from the Russia inquiry, later revealed to be due to his participation in text message conversations critical of Trump with a colleague. ABC News reported Tuesday evening that the texts included messages that the president — still a candidate at the time of the exchanges — was "an idiot."
Rosenstein addressed concerns from congressmen Wednesday that political affiliation could have an impact on the impartiality of the investigation.
"I think it’s important to recognize that when we talk about political affiliation… the issue of bias is something different," he said, adding that he and Mueller "recognize we have employees with political opinions. It’s our responsibility to make sure those opinions do not influence their actions."
The deputy attorney general continued by saying he believes Mueller is leading his office "appropriately."
Appearing to seize upon the news of Strzok's messages earlier this month, Trump commented via Twitter that he believed the FBI's reputation was "in tatters" and the "worst in History," a notion Rosenstein refuted.
"I’ve expressed concern with certain aspects of certain things done by the FBI, but in general throughout my experience working with FBI agents over the decades, I found them to be an exceptional group of public servants, very loyal, faithful and dedicated, and I believe some of the finest people that I know are agents from the Federal Bureau of Investigation," he said in response to committee questioning on the matter.
As for some legislators' ongoing concerns that Trump would order Rosenstein to dismiss Mueller in an attempt to end the Russia investigation, the deputy attorney general said no such suggestion has been raised.
"Nobody has communicated to me a desire to remove Robert Mueller," he said Wednesday.