Political analysts said Mr Trump has benefited from avoiding direct engagement with his Republican rivals.
They suggested that he had delivered a surprisingly “cogent” performance at his own event which took place at the same time as the debate.
Liam Donovan, a former staff member at the National Republican Senatorial Committee, told The New York Times: “Trump’s decision not to indulge and validate the debate exercise was a shrewd move in its own right, but leaving them to tear each other apart is a nice fringe benefit.
“The little lines and digs might please their backers but it’s really tough to imagine any of this appealing to folks looking to make a decision.”
‘She’s gonna get smoked’
On Wednesday, Mr Christie was overheard predicting that Ms Haley would lose badly in an interaction caught on a studio microphone.
Minutes before he ended his own 2024 campaign, Mr Christie said that Ms Haley was “gonna get smoked”.
“She’s not up to this,” he said during a private conversation that appeared to be inadvertently broadcast online, before being deleted, ahead of his town hall in Windham, New Hampshire.
Mr Christie also said that Mr DeSantis had telephoned him “petrified”, at which point the microphone was cut off.
Mr Trump said on Truth Social, the social media platform he founded, that Mr Christie had been caught on a hot mic “making a very truthful statement” about Ms Haley.
Mr Trump’s New York civil fraud trial is back in session on Thursday for closing arguments, as the state’s attorney general seeks nearly $370 million (£303 million) in penalties from the former president for overstating his net worth to banks.
The lawsuit brought by Letitia James alleges that Mr Trump and his associates inflated the value of his assets by billions of dollars to secure better loan terms and other financial benefits for more than a decade.
Mr Trump has denied wrongdoing and said the case is a political witch hunt.