Fellow GOP presidential contender Sen. Lindsey Graham, whose number Trump read to an audience, called him a "jackass," only to see floods of Trump supporters jam his phone line.
Trump is now at odds with much of the Republican establishment after a series of incendiary comments, topped by his weekend mocking of Arizona Sen. John McCain's experience as a tortured prisoner of war in Vietnam.
Since then the real estate developer and reality TV host has intensified his criticism of McCain and his record on veterans issues in the Senate even as politicians from both parties and veterans groups have rushed to his defense.
In a speech to hundreds of supporters in Bluffton, S.C., on Tuesday, Trump kept up that drumbeat, accusing McCain of being soft on illegal immigration.
"He's totally about open borders and all this stuff," Trump said. McCain sparked Trump's temper last week when he said his inflammatory remarks about Mexican immigrants had brought out the "crazies." And, he said Tuesday he would no longer respond to Trump's comments.
Graham, a McCain friend and one of the 16 notable Republicans running for the presidential nomination, betrayed the growing exasperation and anger of many in the party when he appeared earlier on "CBS This Morning."
"Don't be a jackass," Graham said. "Run for president. But don't be the world's biggest jackass."
He said Trump had "crossed the line with the American people" and predicted this would be "the beginning of the end with Donald Trump."
Trump responded during his speech by calling Graham an "idiot" and a "lightweight." He then held up a piece of paper and read out the senator's cell phone number to the capacity crowd of 540 people and the TV audience.
"Give it a shot," Trump encouraged. "He won't fix anything, but I think he'll talk to you."
Graham's voice mailbox was full Tuesday afternoon, said spokeswoman Brittany Brammell. Graham tweeted later: "Probably getting a new phone. iPhone or Android?"
Christian Ferry, Graham's campaign manager said Trump "continues to show hourly that he is ill-prepared to be commander in chief."
The back-and-forth is the latest in a series of showdowns between Trump and fellow GOP candidates frustrated by Trump's brash campaign, which has often overshadowed their own in recent weeks.