That is up from 48 percent approval in the same poll in July and slightly above the same level of support of 55 percent that the poll found in June.
In recent months, Trump and his lawyer Rudolph W. Giuliani have repeatedly disparaged Mueller and his team on social media and in television interviews, accusing the lawyers of bias and conflicts of interest and claiming that they are trying to frame the president.
In a tweet earlier this week, Trump called Mueller “disgraced and discredited” and said his team of prosecutors is “a National Disgrace!”
The Fox News poll is not the only survey that has shown growing or solid support for the Mueller probe.
A poll released by CNN/SRSS earlier this month found 47 percent of voters approved of how Mueller is handling the Russia investigation, up from 41 percent in June.
Meanwhile, a Quinnipiac poll this month showed a slight drop-off in the percentage of voters who think Mueller in conducting a fair investigation, to 51 percent from 55 percent in July.
And in a Washington Post-Schar School poll in July, 49 percent of adults approved of the Mueller investigation, while 45 percent disapproved. The question has not been posed in a Post-Schar poll since then.