"We have sixty-seven counties in this state, each of which conduct their own elections. I promise you there is not a sixty-seven county conspiracy to rig this election," he said.
"There is no evidence behind any of this, so this should not continue to be said," Rubio added.
As he continues to trail Clinton is recent polling, Trump has increasingly raised the possibility of a rigged election without any evidence, a claim he has made throughout his White House bid.
"The problem is the other party has nominated someone who has violated federal law," he said, arguing that both candidates are flawed.
Asked if there is anything Trump could do to lose his support, Rubio referenced Clinton's mishandling of classified information and use of a private email server as secretary of state.
The Florida Republican also appeared to commit to serving a full six-year term if re-elected - which he had not done before Monday's debate.
"I will serve a full six-year term in the Senate, God willing," Rubio said.
Murphy stood by his absolute support for Hillary Clinton, despite her struggles to earn the trust of American voters.
"Secretary Clinton has already apologized for what she did," he said. "She will hit the ground running on Day One."
He struggled to respond to attacks from Rubio, who criticized his claims of being a small-business owner. Murphy ran a company that is a subsidiary of his father's billion-dollar construction firm.
"It’s not that hard to open a small business when your dad opens it for you," Rubio said, while also bringing up Murphy's father's work building two Trump-branded high rises in South Florida.
Murphy, who has supported Obama's policies toward Cuba, refused to say whether he'd vote to lift the U.S. embargo on the country.