Trump faulted both the Justice Department and Federal Bureau of Investigation for not indicting Clinton over her use of a private email server as secretary of state. FBI Director James Comey cited her careless handling of classified emails but opted not to prosecutor her.
"The Justice Department is required to appoint a special prosecutor because it has proved to be, sadly, a political arm of the White House," Trump said. "Nobody has ever seen anything like it before."
Trump's appeal came the same day a conservative watchdog group, Judicial Watch, released 725 pages of State Department documents, including some it said were examples of preferential treatment provided to donors at the request of former Clinton Foundation executive Douglas Band.
Trump's call for an independent investigation followed an announcement by the Clinton Foundation that it would no longer accept foreign donations should Clinton be elected president.
The Clinton campaign fired back at Trump, saying the foundation had already laid out "the unprecedented steps the charity will take if Hillary Clinton becomes president."
Clinton campaign chairman John Podesta said in a statement that Trump "needs to come clean with voters about his complex network" of businesses that are in debt to big banks, including the state-owned Bank of China, after a New York Times report on the subject.
"Donald Trump should stop hiding behind fake excuses and release his tax returns and immediately disclose the full extent of his business interests," Podesta said.
Seeking to expand base
While keeping up the attack on Clinton, Trump in his speech also outlined some agenda items, as Republicans have been urging him to do for months. The more disciplined Trump followed a campaign shake-up last week that brought in veteran pollster Kellyanne Conway as campaign manager.
But in a sign that organizational challenges remain, Trump canceled a rally planned for later this week in Las Vegas and postponed an immigration speech in Denver.
Earlier on Monday, Trump insisted he was not "flip-flopping" on immigration, despite a comment by Conway on Sunday that his plan to deport 11 million illegal immigrants was still under review.
In his Akron remarks, Trump, struggling to broaden his support beyond the white working-class voters who have been his base of support, again urged blacks and Hispanics to give him a chance, saying: "What the hell do you have to lose?" repeating a line he delivered on Friday that was criticized by Clinton as "ignorant."
Trump said Democratic politicians had not been able to stem crime and poverty in inner cities despite pledges to do every election year.
"I say it and I'm going to keep saying it and some people say: 'Wow that makes sense' and some people say: 'That's not very nice,'" Trump said. "And I say it with such a deep-felt feeling, what do you have to lose? We'll bring jobs back. We'll bring spirit back. We'll get rid of the crime."