"There have been irregularities in our elections, sometimes even fraud, but never to an extent that it affected the outcome," McCain wrote in the statement. "We should all be proud of that, and respect the decision of the majority even when we disagree with it. Especially when we disagree with it."
He cited his own loss and subsequent concession in the 2008 election as an example.
"I didn’t like the outcome of the 2008 election. But I had a duty to concede, and I did so without reluctance," McCain wrote. "A concession isn’t just an exercise in graciousness. It is an act of respect for the will of the American people, a respect that is every American leader’s first responsibility."
While the statement did not mention Donald Trump, McCain's campaign released it in the wake of a wave of backlash to Trump's refusal during the final presidential debate on Wednesday to commit to accepting the results of the election in November.
When asked by moderator Chris Wallace if he would accept the results of November’s election, Trump said he will "will look at it at the time."
"I will keep you in suspense, okay?” he added.