In the latest poll, Lula received 47 per cent of voter support against Bolsonaro's 32 per cent, compared with 47 per cent and 29 per cent respectively in July.
In a potential second-round runoff between the two candidates, the poll added, Lula would return to the office with 54 per cent of the votes against Bolsonaro's 37 per cent.
Lula, a leftist candidate and a former Brazilian president, has seen his advantage shrink each month from the 29 points lead he had in December, the poll said.
In Rio de Janeiro, Ricardo Ismael, a local, said he didn’t trust the poll’s results as he believes Bolsonaro will finally be reelected in the runoff.
Far-right President Jair Bolsonaro and his leftist front-running challenger Luiz Inacio Lula da Silva formally launched their campaigns on Tuesday (August 16) for Brazil's most polarized elections in decades in October.
The race pits a nationalist-populist with an agenda backed by Christian conservatives against a former union leader and two-term president of the country (2003-2010) who was jailed for corruption until his convictions were annulled.