Analysts expect higher US output to offset supply curbs by the Organization of the Petroleum Exporting Countries, which have been in place for 18 months and have pushed up prices significantly over the last year.
Benchmark Brent crude was down 15 cents at $ 76.31 a barrel by 0915 GMT. US light crude was 10 cents lower at $ 65.64.
The number of new rigs drilling for oil in the United States rose by one last week to 862, its highest since March 2015, data from energy services firm Baker Hughes showed.
That implies US crude output, already at a record high of 10.8 million barrels per day (bpd), will climb further.
Russian news agency Interfax said on Saturday Russia’s oil production had risen to 11.1 million bpd in early June, up from slightly below 11 million bpd for most of May, and well above its target output of under 11 million bpd.
But markets are worried by falling supply from Venezuela and the potential of lower exports from Iran.
Venezuelan production is falling due to sanctions, economic crisis and mismanagement, while Iran faces US sanctions over its nuclear programme that are likely to curb exports in the next few months.
“Sentiment is caught in a tug of war between the drop in supply from Iran and Venezuela and the prospect of rising output from Opec/non-Opec coupled with rampant US shale production,” said Stephen Brennock, analyst at brokerage PVM Oil Associates.
Opec, together with some non-Opec producers including Russia, started withholding output in 2017 to try to end a global supply glut and support prices.
“Non-Opec supply is expected to rise sharply in 2019 led by US shale growth, along with Russia, Brazil, Canada and Kazakhstan,” US bank JPMorgan said, adding that it was bearish for oil in the second half of this year.
“Oil fundamentals are expected to weaken in 2019 on the back of stronger-than-expected non-Opec supply, but also the potential release of barrels from Opec as the joint accord between Opec and non-Opec is unlikely to stay in place,” JPMorgan said in its quarterly outlook.
Opec and its partners are due to meet on June 22-23 in Vienna.