* U.S. rig count rises to 820, highest since March, 2015
* But strong demand, OPEC cuts still support prices overall
By Henning Gloystein
SINGAPORE, April 23 (Reuters) - Oil prices dipped early on Monday as a rising U.S. rig count pointed to further increases in the country's output, underlining one of only a few factors holding back crude markets in an otherwise bullish environment.
Brent crude oil futures were at $73.87 per barrel at 0031 GMT, down 19 cents, or 0.3 percent, from their last close.
U.S. West Texas Intermediate (WTI) crude futures were down 23 cents, or 0.30 percent, at $68.17 a barrel.
U.S. drillers added five oil rigs drilling for new production in the week ending April 20, bringing the total count to 820, the highest since March, 2015, according to General Electric's Baker Hughes energy services firm. The rising rig count points to further increases in U.S. crude production C-OUT-T-EIA, which has already climbed by a quarter since mid-2016 to a record 10.54 million barrels per day (bpd).
Only Russia currently produces more, at almost 11 million bpd.
Despite the dips in crude oil prices on Monday, overall markets remain well supported by strong demand, especially in Asia, and Brent prices are up by 20 percent from their 2018 lows in February.
Providing further support have been supply cuts led by the Organization of the Petroleum Exporting Countries (OPEC) introduced in 2017 with the aim of propping up prices, as well as by the potential of renewed U.S. sanctions against Tehran.
The United States has until May 12 to decide whether it will leave the Iran nuclear deal, which would further tighten global supplies.
"Stay long oil," U.S. bank J.P. Morgan said in a note to clients.
Reporting by Henning Gloystein Editing by Joseph Radford