The President of Brazil, Luiz Inácio Lula da Silva, has cancelled a visit to the southern state of Santa Catarina because his Argentine counterpart is there this weekend.
Javier Milei is expected to meet Brazil’s former President Jair Bolsonaro at a gathering of conservative leaders.
Lula recently demanded an apology from Mr Milei, who had described him as corrupt, a communist and a dinosaur.
Mr Milei said he “had no regrets”. The leaders of South America’s two biggest economies have never talked face to face.
Mr Milei, a right-wing economist and former television personality, is expected to attend a meeting of the Conservative Political Action Conference in Santa Catarina.
At the gathering, he plans to meet Mr Bolsonaro, whom Lula defeated in the 2022 Brazilian presidential election.
Mr Milei is an outspoken critic of leftist governments in the region.
During his successful election campaign last year, he accused Lula of being corrupt.
The current Brazilian president once spent a year and a half in prison for corruption but the charges were dismissed on appeal. After his release he was allowed to run for office again.
Last week, Lula demanded an apology from Mr Milei but the Argentine leader ruled that out, saying: “I haven’t done anything wrong.”
The main concern among diplomats and businessmen is that the row between the leaders of the two neighbouring countries will have a major impact on bilateral relations.
Brazilian news website UOL said Mr Milei was putting the future of the South American trade bloc Mercosur at risk.