With dueling appearances in Arkansas and Georgia, the billionaire businessman and US senator from Florida continued an onslaught of personal insults that began on a debate stage on Thursday and looks likely to continue for months.
"The majority of Republican voters do not want Donald Trump to be our nominee, and ... they are going to support whoever is left standing that is fighting against him to ensure that we do not nominate a con artist," Rubio told reporters in Georgia.
Trump, speaking in front of his private plane in Arkansas, along with Christie, whose endorsement on Friday shocked Republican leaders anxious about his likelihood of winning the nomination, belittled Rubio and accused him of being fresh.
"I watched this lightweight Rubio, total lightweight, little mouth on him, 'bing, bing, bing' ... and his new attack is he calls me a con artist," Trump said.
"The last thing I am is a con man."
Their back and forth came while voters went to the polls in South Carolina's Democratic presidential primary between Hillary Clinton and Bernie Sanders, taking place a week after South Carolina's Republican primary.
Former Secretary of State Clinton is expected to beat Sanders handily there. The state's large African-American population is expected to favor her over Sanders, a US senator from Vermont.
A big win would give Clinton added momentum ahead of Tuesday, when roughly a dozen US states make their choices for the Democratic and Republican presidential nominations.
Establishment worries, Cruz predicts doom
With hundreds of delegates at stake in Tuesday's contests, the day could be a critical turning point for candidates in both parties.
Nominations in both parties are contingent on winning a majority of the votes by the delegates sent to the party conventions in July.
The Tuesday contests could upend the Republican race further if underperforming candidates drop out. Ted Cruz, the US senator from Texas who won the Iowa nominating contest, must do well in his home state on Tuesday to regain momentum. Texas will send 155 delegates to the Republican National Convention, more than 10 percent of the 1,237 delegate votes needed for the party's nomination.
Ohio Governor John Kasich, who is behind in the polls, said his state's contest on March 15 would determine whether he stays in the race.
With the high-profile exception of Christie, many "establishment" Republicans have coalesced around Rubio in the hope of stopping Trump from gaining their party's mantle in the general election.
Rubio stopped short of calling on his fellow candidates to drop out on Saturday.
"When voters have a clear choice between two people, that's when Donald Trump starts to lose, so the sooner that happens, the better off we're going to be as a party," he said.
Rubio, who has criticised Trump for resisting releasing his tax returns, had not released his own by Saturday afternoon.
He said Trump did not want his to be made public because they might reveal him to be less wealthy than believed.
"I think part of it is he's not as rich as he says he is,"Rubio said.
At a campaign rally in Georgia, Cruz said a Trump victory would doom the party's chances of winning the White House.
"If we nominate Donald, we end up electing Hillary as president," he said.
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