The CNT/MDA poll said 40.6% of the people surveyed said the performance of the Lula government was "great" or "good" compared with 43% in the previous poll in May.
Lula narrowly defeated Bolsonaro in a runoff election last October and took office in January.
Still, 46% of those polled say the new government is better than Bolsonaro's, which had a 12-percentage-point lower approval rating after nine months in office.
Approval of Lula's own performance as president has also dipped, to 54.9% from 57%, with disapproval rising to 39% from 35%.
MDA, commissioned by the national transport lobby CNT, polled 2,002 people across Brazil between Sept. 27 and Oct. 1.
Persons:
Luiz Inacio Lula da Silva's, Jair Bolsonaro, Lula, Marcelo Souza, Bolsonaro, Anthony Boadle, Steven Grattan, Rod Nickel
Organizations:
CNT, MDA, Thomson
Locations:
BRASILIA, Brazil, Brasilia