According to the poll, which randomly sampled 1,002 adults, 69 percent support Mueller's investigation into possible collusion between the Trump campaign and Russia, while 25 percent oppose the investigation.
Additionally, 64 percent of Americans support the investigation into Trump's business dealings, with 32 percent in opposition. Fifty-eight percent support the investigation into claims that Trump's associates paid women to remain quiet about their alleged affairs with the president, with 35 percent in opposition.
Women are also less likely than men to support the president, according to the poll.
The poll found that 65 percent of women supported Mueller's hush-money investigation, while only 50 percent of men supported it. Women were also five points more likely than men to support the Russia probe and eight points more likely to support the investigation into Trump's business dealings.
Trump has repeatedly denied that there was collusion between his campaign and Russia, calling Mueller's probe a "witch hunt." He has also denied knowing about the $130,000 payment that his personal attorney, Michael Cohen, made to adult film star Stormy Daniels.
Citizens were also polled on former FBI Director James Comey, who Trump fired in May 2017. Only 33 percent approved of Trump's decision to fire Comey, with 47 percent disagreeing with the decision. Citizens were also more likely to believe Comey than Trump, with 48 percent stating that they believed Comey, compared with the 32 percent that said they believed Trump.
The poll data was released just as shocking details about Trump from Comey's memoir, "A Higher Loyalty," surfaced in the media.
The White House did not immediately respond to CNBC's request for comment.