Trump said "now that I am the presumptive Republican nominee, it seems inappropriate that I would debate the second place finisher", referring to Sanders, who is running behind Hillary Clinton in the race to the White House in the Democratic Party.
He alleged that the Democratic nominating process is totally rigged and "Crooked Hillary Clinton" and Deborah Wasserman Schultz, the head of the Democratic National Committee, will not allow Sanders to win.
"Likewise, the networks want to make a killing on these events and are not proving to be too generous to charitable causes, in this case, women's health issues.
"Therefore, as much as I want to debate Bernie Sanders --- and it would be an easy payday -- I will wait to debate the first place finisher in the Democratic Party, probably Crooked Hillary Clinton, or whoever it may be," he said in a statement on Friday.
This came as a surprise move after saying he would "love to debate" with Sanders on Thursday, triggering wild speculation and media frenzy.
Trump had asked for at least $10 million for charity from the hosting television channel.
However, Sanders in a statement alleged that Trump is running away from participating in a debate with him, saying there is a "reason" why the billionaire is doing so which the Americans should be "able to see it up front in a good debate".
"In recent days, Donald Trump has said he wants to debate, he doesn't want to debate, he wants to debate and, now, he doesn't want to debate.
"Given that there are several television networks prepared to carry this debate and donate funds to charity, I hope that he changes his mind once again and comes on board," Sanders said.
"There is a reason why in virtually every national and statewide poll I am defeating Donald Trump, sometimes by very large margins and almost always by far larger margins than Secretary Clinton.
"There is a reason for that reality and the American people should be able to see it up front in a good debate and a clash of ideas," he said.
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