MEXICO CITY, Sept 23 (Reuters) - Crude oil production at Mexican state oil firm Pemex dipped in August compared with the previous month, while exports rose, the company said on Friday.

Crude output at Pemex averaged 2.144 million barrels per day (bpd) in August, a decline of 0.6 percent from July, according to figures published on the company's website.

Exports of crude rose by 10 percent to 1.261 million bpd.

Crude output at Pemex, which now faces private sector competition since losing its monopoly in 2013, has dipped steadily since peaking at around 3.4 million bpd in 2004.

(Reporting by Dave Graham; Editing by Leslie Adler)