The simmering animosity between Donald Trump and Ron DeSantis, the Florida governor emerging as Trump’s most likely challenger for the 2024 Republican presidential nomination, looks set to evolve into open warfare following the midterm elections.

Polls show DeSantis comfortably positioned to win re-election on Tuesday but political opponents say his focus is locked on the national stage and a White House run.

The two Republicans’ feuding became evident during a rally for Senate candidate Mehmet Oz in Pennsylvania on Saturday, when Trump, who is expected to announce his presidential campaign imminently, introduced his new nickname for the rising conservative star: Ron DeSanctimonious.

It is a tactic that has cowed previous pretenders to Trump’s crown as the Republican leader and kingmaker. In the 2016 election cycle, senior Republican hopefuls “Little Marco” Rubio, “Lyin’ Ted” Cruz and “Low Energy” Jeb Bush were derided then swept aside.

“There it is, Trump at 71. Ron DeSanctimonious at 10%,” Trump said in Pennsylvania as he perused a screen showing what he claimed were approval ratings for the Republican 2024 nomination.

“Mike Pence at seven. Oh, Mike’s doing better than I thought,” Trump added, mocking his former vice-president who he has castigated for refusing to endorse the lie that his 2020 defeat by Joe Biden was the result of electoral fraud.

With no discernible irony, Trump called Rubio “my great friend” at a rally for the senator and other Republican candidates in Miami on Sunday, an event at which DeSantis was conspicuously absent.

Until now, DeSantis and Trump have mostly kept each other at arm’s length. But clues to their fractured relationship were evident as early as August 2020, when the notoriously prickly DeSantis denounced as “a phony narrative” an assertion he was the then-president’s “yes man” in Florida.

The governor subsequently criticized Trump’s handling of the Covid-19 pandemic, saying earlier this year he regretted “not speaking out” sooner against Trump’s call for a nationwide lockdown. In response, Trump called DeSantis “gutless” for refusing to reveal if he had been given a Covid booster vaccine.

In June, Trump began readying his anti-DeSantis rhetoric, telling the New Yorker he would beat his rival in a nomination contest and claiming it was only his endorsement that revived the three-term congressman’s faltering campaign for governor in 2017.

Now, with the distraction of the midterms almost out of the way, and with Trump seeking a clear run for his third presidential run as a Republican, DeSantis too has been granted a derogatory nickname.

DeSantis’s apparent focus on 2024 – notwithstanding reports he has told donors he may wait until 2028, when Trump will be out of the way – became an issue during the governor’s debate in Florida last month. Charlie Crist, the Democratic nominee, repeatedly challenged DeSantis to say if he would commit to a full four-year term if re-elected.

Seizing on DeSantis’s refusal to answer, Crist said: “It’s not a tough question. It’s a fair question. He won’t tell you.”

DeSantis described Crist, a Republican Florida governor turned Democratic congressman, “a worn out old donkey” he was looking to “put out to pasture”.

At the Miami rally on Sunday, Trump declined to criticize DeSantis again but offered only tepid support for him in Tuesday’s elections, compared to his comments about Rubio and other Republicans in congressional and state races.

“You’re going to re-elect the wonderful, the great friend of mine, Marco Rubio to the United States Senate. And you are going to re-elect Ron DeSantis as your governor,” Trump said.

Despite Trump’s attacks, DeSantis remains in a strong position, winning straw polls of grassroots supporters and becoming ever more visible on the national stage.

According to Politico, he also has the backing for any presidential run of the Republican mega-donor Ken Griffin, who donated more than $60m to the party’s candidates during the midterms.

“I don’t know what he’s going to do. It’s a huge personal decision,” Griffin said. “He has a tremendous record as governor of Florida, and our country would be well-served by him as president.”