The agency also revised its estimate for May up by 1,000 bpd to 10.4 million bpd.
US crude production has been increasing, nearing top producers Russia and Saudi Arabia. Saudi Arabia produced 10.5 million bpd in August, according to a Reuters survey. Russian output was seen at 11.2 million bpd in July, and was expected to hold that level in August.
US output has been closely watched by crude oil markets, which have contended with concerns about oversupply as oil production ramps up and trade tensions between the United States and China weigh on global demand forecasts.
The gains reflected growing production onland in Texas, where output climbed 165,000 bpd, or 3.9 percent, to 4.4 million bpd. Output also rose in the Gulf of Mexico, climbing 10.3 percent, or 154,000 bpd to 1.7 million bpd.
Crude and refined products exports rose from a month earlier. Crude oil exports rose nearly 200,000 bpd in the month, hitting a fresh record of 2.2 million bpd, more than twice the level seen in June a year ago.
Gasoline demand in June increased 0.3 percent, or 32,000 bpd, from a year earlier to 9.8 million bpd, compared with a 0.4 percent decline in May. Distillate demand fell 0.4 percent, or 15,000 bpd to 4 million bpd, compared with a 7.7 percent rise in May, according to the Petroleum Supply Monthly report.
US natural gas production in the lower 48 states rose to an all-time high of 90.8 billion cubic feet per day (bcfd) in June, up from the prior record of 89.9 bcfd in May, according to EIA's 914 production report.
Output in Texas, the country's largest gas producer, increased 1.5 percent in June to 23.9 bcfd.
In Pennsylvania, the second biggest gas producing state, production rose 2.2 percent to 16.5 bcfd in June. The United States has been the world's biggest producer of gas since 2009, ahead of Russia.