A 58 percent majority say they approve of Mueller's handling of the investigation, while 28 percent say they disapprove, the Post-ABC poll finds. People's views depend in large part on their political leanings, but overall, Americans are generally inclined to trust Mueller and the case he has made so far.
Meanwhile, fewer than 4 in 10 Americans say they believe Trump is cooperating with Mueller's investigation, while about half believe he is not.
A similar 49 percent think it is likely Trump himself committed a crime in connection with possible Russian attempts to influence the election, although more say this view is based on suspicion rather than on hard evidence.
Mueller's investigation entered a new phase this week as he revealed charges against three former Trump campaign officials: former campaign chairman Paul Manafort, his longtime business partner Rick Gates, and foreign policy adviser George Papadopoulos.
Manafort and Gates were charged with crimes unrelated to their campaign work. In a 12-count indictment, the special counsel alleged that they engaged in a conspiracy to launder money and defraud the United States, stemming from their attempts to hide their work advising a Russia-friendly political party in Ukraine.
Papadopoulos, meanwhile, pleaded guilty to lying to FBI agents about the nature and timing of his conversations with foreigners claiming to have high-level Russian connections. His plea, which was unsealed Monday, describes how he had extensive talks to try to broker a meeting between campaign and Russian officials, and high-level members of the campaign seemed to entertain what he was doing — though some seemed to be wary.
The poll finds strong backing for the charges against Manafort and Gates — nearly 7 in 10 approve — and a general suspicion that more is to come.
A narrow 53 percent majority say those charges and the plea by Papadopoulos for lying to the FBI represented broader wrongdoing by people involved in Trump's campaign, while 28 percent think they are limited to these instances.
A spokesman for Mueller's office declined to comment, and a White House lawyer did not immediately return messages.
Mueller and Trump have notably different styles, with the president often airing his grievances publicly, while the special counsel works largely in secret. Trump was said to have fumed Monday at news of charges in the case, and on Twitter, he tried to cast the case against Manafort and Gates as unconnected to him.
"Sorry, but this is years ago, before Paul Manafort was part of the Trump campaign. But why aren't Crooked Hillary & the Dems the focus?????" he wrote, adding minutes later, "....Also, there is NO COLLUSION!"
The president and his surrogates have long sought to raise questions about the credibility of Mueller and his team. In the summer, they focused on the people Mueller was hiring, noting that many had donated to Democratic political candidates and Trump's opponent in the presidential election, Hillary Clinton.
In a June 15 tweet, Trump called the probe the "single greatest WITCH HUNT in American political history," adding that it was "led by some very bad and conflicted people!"
More recently, Trump and his allies, buoyed by conservative media, have tried to point attention toward the Clinton campaign's role in funding the production of a salacious dossier about Trump — which was prepared by a former British spy who got information from Russian sources. The special counsel has explored some of the allegations in the dossier.
Conservatives have also sought to highlight Clinton's alleged role in approving the sale of a Canadian company with mining rights in the United States to Russian's nuclear energy agency.
The Post-ABC poll finds politics influences people's responses, with 78 percent of Democrats and 56 percent of independents approving of the way Mueller is handling the investigation, compared with 38 percent of Republicans.
People on both sides of the aisle are more unified in supporting the particular charges against Gates and Manafort. A 57 percent majority of Republicans say they approve of that case, as do 78 percent of Democrats.
Manafort and Gates have pleaded not guilty, and in a court filing Thursday, attorneys for Manafort asserted that the evidence against him had "been embellished."
Partisanship also colors how people perceive the significance of Mueller's charges, with more than three-quarters of Democrats saying they represent "broader wrongdoing" by people involved in the Trump campaign, compared with a small majority of independents.
Republicans are less united, with 46 percent saying wrongdoing is limited to Manafort, Gates and Papadopoulos and 30 percent saying they suspect broader misconduct. Almost a quarter of Republicans say they have no opinion.
An 82 percent majority of Republicans say it is unlikely that Trump himself committed a crime, although half of independents and 74 percent of Democrats say that is likely. Among the public overall, 19 percent think there is "solid evidence" Trump committed a crime, while 30 percent say that is merely their suspicion.
Among Democrats, a 30 percent minority believe there is solid evidence Trump committed a crime.
Trump had in the past inquired about his power to pardon aides, and Democrats have feared he might move to fire Mueller before the probe is complete. White House press secretary Sarah Huckabee Sanders, though, said this week that Trump had "no intention or plan to make any changes with regard to the special counsel." And Ty Cobb, a White House lawyer overseeing the administration's handling of the Mueller probe, said there had been no talk of possible pardons for Manafort or Gates.
The Post-ABC poll was conducted Oct. 30-Nov. 1 among a random national sample of 714 adults reached on cell and landline phones. The poll has a margin of sampling error of plus or minus 4.5 percentage points.
Scott Clement contributed to this report.