"Crazy Bernie has just entered the race. I wish him well!" Trump said, using the same nickname he used to deride Sanders when he sought the Democratic presidential nomination in 2016.
Sanders, a self-described democratic socialist, responded on Twitter shortly afterward.
"What's crazy is that we have a president who is a racist, a sexist, a xenophobe and a fraud," he wrote. "We are going to bring people together and not only defeat Trump but transform the economic and political life of this country."
Sanders announced his second White House bid yesterday, calling Trump "the most dangerous president in modern American history."
Trump sized up Sanders' prospects for reporters in the Oval Office, saying, "Personally, I think he missed his time."
"It will be interesting to see how he does," Trump added.
Sanders ran a surprisingly robust primary campaign in 2016, extending the race well beyond what Hillary Clinton's team had expected.
"I think what happened to Bernie maybe was not so nice," Trump told reporters. "I think he was taken advantage of. He ran great four years ago, and he was not treated with respect by Clinton."
In an email to supporters, Sanders said he would push some of the same issues in his new run for the White House that animated his 2016 bid, including healthcare, climate change, student debt and income inequality.
Trump made a habit of using nicknames for his opponents in 2016, including Clinton - whom he dubbed "Crooked Hillary" - and several Republicans.
Trump, for example, regularly referred to GOP primary opponent Senator Ted Cruz of Texas as "Lyin' Ted" and former Florida Governor Jeb Bush as "low energy."
As the 2020 race gears up, Trump has continued to refer to Senator Elizabeth Warren as "Pocahontas," a reference to a controversy over her claims of Native American heritage.
