SAO PAULO, Aug 11 (Reuters) - Brazilian state-run oil company Petrobras said on Thursday it will lower refinery gate diesel prices by 4% starting Friday, the second cut in a week, which drew praise from President Jair Bolsonaro.

Bolsonaro and federal lawmakers pressured Petrobras to bring down soaring fuel prices as inflation surged ahead of a general election in October.

Petroleo Brasileiro SA, as the company is formally known, said in a statement on its website it will cut diesel prices to 5.19 reais ($1.01) from 5.41 reais, while gasoline prices were kept unchanged.

Petrobras shares were down 0.3% by midday, underperforming Brazil's Bovespa stock index, even as global crude prices rebounded from a recent slump.

Bolsonaro cheered the price cut as a "very relevant act in favor of Brazil and its people," a reference to manifestos read by business leaders and intellectuals earlier in the day defending democratic institutions.

Last week, the oil company lowered diesel prices by 3%, the first downward adjustment in more than a year.

Analysts at Credit Suisse said Petrobras was catching up with an appreciated Brazilian real and international market conditions. They estimated local diesel prices at a 3% premium over the import parity.

Ativa Investimentos analyst Ilan Arbetman the two successive cuts still might raise queries on how Petrobras is positioned to protect itself from market swings.

Petrobras repeated the same communication it used last week, saying the move was in line with its fuel pricing policy - which pegs local prices to international rates - and reflected global benchmark prices stabilizing at a lower level for diesel.

Falling fuel prices and tax cuts were among the main reasons for Brazil to report its largest monthly drop ever in consumer prices in July. ($1 = 5.1449 reais) (Reporting by Gabriel Araujo; Editing by Christian Plumb and David Gregorio)