(CNN) - Robert Mueller continues to merit more positive than negative reviews for his handling of the Russia investigation, while President Donald Trump's marks on handling it remain majority negative, according to a new CNN poll conducted by SSRS.
The public does agree with one recent Trump decision on Russia: 53% say he should not fire Deputy Attorney General Rod Rosenstein. Just 18% of Americans think Trump should fire the senior Justice Department official who oversees the Russia investigation.
Related: Full poll results
That threat seems to have passed, for now, but in late September, the two appeared to be on a collision course after The New York Times reported Rosenstein had secretly discussed the possibility of recording conversations with Trump and of using the 25th Amendment as a way to remove Trump from office.
Rosenstein had offered his resignation and had at one point expected to be fired. But the climax of Brett Kavanaugh's Supreme Court nomination was a distraction and Rosenstein has remained in his post.
While the poll shows a majority overall opposed to Trump pulling the plug on the Deputy AG, there are sharp differences by party. Among Republicans, 27% say the President should fire Rosenstein, 39% that he should not, with another 34% saying they're not sure what the President should do. Democrats are firmly anti-firing: 72% say Rosenstein shouldn't be fired vs. 12% who think he should be.
Overall, about six in 10 say the Russia investigation is a serious matter that should be fully investigated, while about a third consider it mainly an effort to discredit Trump's presidency. Those figures have held steady in the last month.
The public's approval ratings for Mueller (48% approve, 36% disapprove) and the President (33% approve, 54% disapprove) have also held roughly even in the last month.
The CNN Poll was conducted by SSRS October 4 through 7 among a random national sample of 1,009 adults reached on landlines or cellphones by a live interviewer. Results for the full sample have a margin of sampling error of plus or minus 3.8 percentage points.