The poll also indicated a large gap in opinion exists across partisan lines with 67 percent of Democrats saying they believe ousting Mueller would be inappropriate versus 11 percent who say otherwise.
The divide among Republicans is narrower, with 37 percent saying it would be appropriate to fire Mueller versus 29 percent who say it would not.
Media in the United States has speculated that Trump may consider dismissing US Attorney General Jeff Sessions, whom the president heavily criticized last week, over his recusal from the Russia investigation. Appointing a new attorney general would enable the Trump administration to remove Mueller.
Russia has repeatedly refuted allegations of meddling in the US election and has called them absurd.
The poll was conducted July 20-24 among nearly 4,000 registered voters and has a margin of error of plus-minus 2 percentage points.
