Brazil has recalled its ambassador to Buenos Aires after Argentina's president hit out at the Brazilian president, referring to him as a "thief" and a "convict".

Javier Milei made the comments on Sunday at a rally in Sao Paulo to launch the presidential campaign of right-wing candidate Flávio Bolsonaro, who is set to run in an election in October.

Without naming Luiz Inácio Lula da Silva explicitly, he referred to the Brazilian president derogatorily while speaking alongside Bolsonaro, who he went on to say was the only one who could "stop Lula".

Brazilian diplomats later said the Argentine leader had insulted Brazil's government, its people, and its democracy.

Speaking later on Sunday, Lula said he would continue to lead "without anyone's interference," and that "in Brazil, we do not accept anyone sticking their nose where it doesn't belong".

Brazil's ambassador to Argentina, Julio Bitelli, was due to return home between Sunday and Monday, AFP reported.

Flavio Bolsanaro is the son of Brazil's former president, Jair Bolsonaro, who was last year sentenced to more than 27 years in jail for plotting a coup aimed at keeping him in power after he lost the last election to Lula.

The judge who oversaw the conviction of Jair Bolsonaro, Brazilian Supreme Court Justice Alexandre de Moraes, was also referred to by Milei as "bald trash".

Moraes had also previously denied Milei permission to visit the former president while he was under house arrest in Brasilia.

In 2018, Lula was sentenced to 12 years in prison over a massive corruption and bribery scandal, but was released after serving a little over 18 months.

Lula's convictions were annulled by the Supreme Court in 2021, and in presidential elections the following year he narrowly beat far-right incumbent Jair Bolsonaro, winning 50.9% of the vote.