Petrobras said it credited May's production increase to the launch of operations at four new platforms in the offshore Campos Basin.
In the Campos and Santos basins alone, Petrobras said oil production increased 8.8 percent from May to 447,000 bpd, a monthly record.
Brazil ranks second behind Venezuela in proven oil reserves in South America. Offshore production is complicated because much of the oil reserves lie beneath a thick layer of salt.
Petrobras, formally known as Petroleo Brasileiro, has struggled with production levels in the past, but attributed the declines to scheduled maintenance at its offshore fields.
The company in a statement Tuesday said new production systems are expected to enter into service this year. A four-year business management plan envisions a 7.5 percent rise in production by the end of 2014, plus or minus one percent.