After reducing output in May to 9.8 million bpd from April's 30-year high of 10.1 million bpd, the world's largest oil exporter raised production again in June, the source said on Wednesday.
Internal demand for Saudi crude rises sharply in the hot summer months from June to August. Export volumes were not available. In addition to the 10.1 million bpd pumped from Saudi fields, the kingdom topped supplies up last month with about 200,000 bpd from storage, the source added.
OPEC ministers at a meeting in mid-June said they would adhere to a collective production limit of 30 million bpd, implying a 1.6 million bpd cut from actual supply of 31.5 million, and Saudi Arabia was expected to make a sizeable contribution to that cut.
The 12-member OPEC group's collective output remained close to its highest levels since early 2008 in June, driven by strong Saudi and Iraqi output, according to a Reuters survey.
A big drop in supplies was seen from Iran as the European Union embargo that took effect on July 1 further limited the Islamic republic's production.
Brent crude rose to near $99 a barrel on Wednesday, recovering slightly from the previous session's fall, ahead of US inventory data that is expected to show crude stocks shrank for a third week in the world's largest oil consumer.