The suggested debate would have sidelined likely Democratic nominee Hillary Clinton but given Sanders a huge platform ahead of California's June 7 primary.
A day after saying he would welcome a debate with Sanders, Trump called the idea "inappropriate" because as the Republican presumptive nominee he should only face the Democrats' final choice.
"I will wait to debate the first place finisher in the Democratic Party, probably Crooked Hillary Clinton," Trump said in a statement.
Sanders’ campaign has been aggressively advocating for a debate with Trump after the idea was raised during an appearance by the New York billionaire on a talk show this week.
Sanders, a U.S. senator from Vermont, expressed disappointment on Friday.
"I heard that he was going to debate me, then I heard that he was not going to debate me, then I heard that he was going to debate me. Now you’re telling me that he is not going to debate me. Well, you know, I hope that he changes his mind again," Sanders said in a video clip posted on an ABC News Twitter account.
Trump suggested broadcast networks were unwilling to go along with his demand that at least $10 million raised from the encounter be donated to charity.
“I’d love to debate Bernie,” he told a rally in Fresno, California. “But the networks want to keep the money for themselves.”
Sanders is trailing Clinton in the race to secure their party’s nomination. Opinion polls show he is slicing into Clinton’s lead in California.
Clinton has shown no interest in debating Sanders before the California primary, which will be part of a final slate of nominating contests. It is possible she will clinch the nomination by winning New Jersey earlier that day, making the outcome in California superfluous.
The former U.S. secretary of state has said she is looking forward to debating Trump later this year ahead of the Nov. 8 general election.
Clinton leads Trump by 4 percentage points in the most recent Reuters/Ipsos poll, with their positions with voters basically unchanged since Trump’s support surged two weeks ago. Democrats nationally remain evenly split between Clinton and Sanders.