Cruz is calling on Trump to convert Tuesday night's planned back-to-back CNN town hall events featuring both candidates into a two-hour debate.
Responding on Twitter, Trump declined in his typically brash fashion: "Lyin' Ted Cruz is weak & losing big so now he wants to debate again. But according to Drudge, Time, online polls, I have won all debates."
At one point in the race, after the first two nominating contests gave Clinton a tight win in Iowa and a blowout loss in New Hampshire, she actually assuaged nervous supporters and agreed to add several more debates with Sanders.
There have been eight debates on the Democratic side, and 12 on the Republican side.
There are still two more debates the campaigns have agreed to on the Democratic side, but they have not yet been scheduled. Sanders is calling for one of them to take place in Clinton's adopted home state of New York, which votes on April 19.
The Sanders campaign released a video on Twitter of Clinton during the 2008 presidential campaign when the roles were reversed and she was trailing then-Sen. Barack Obama. The video shows Clinton challenging Obama to a debate "any time, anywhere."
For the Republicans, a planned 13th debate had been scheduled for March 21, but Trump refused to attend, saying there had been "enough debates." After Trump dropped out, so too did Ohio Gov. John Kasich, prompting moderators to cancel the event.