* US drillers add to rig count for 10th straight week
* Iraq raises prices for its Feb Basra Light crude
Oil prices fell on Monday as increased exports from Iran undermined efforts by other oil producers to curb a global fuel supply overhang and as US drillers increased activity for a 10th straight week.
Brent crude futures, the international benchmark for oil prices, were trading at $56.84 per barrel at 0535 GMT, down 26 cents from their last close.
US West Texas Intermediate (WTI) crude oil futures were trading at $53.70 per barrel, down 29 cents.
Traders said the lower prices were a result of rising exports from Iran that come just as other members of the Organization of the Petroleum Exporting Countries Opec) cut supplies in an effort to end a global glut.
Iran has sold more than 13 million barrels of oil held on tankers at sea, capitalising on an OPEC output cut deal from which it is exempted to regain market share and court new buyers, according to industry sources and data.
The amount of Iranian oil held at sea has dropped to 16.4 million barrels, from 29.6 million barrels at the beginning of October, according to Thomson Reuters Oil Flows data.
Before that sharp drop, the level had barely changed in 2016; it was 29.7 million barrels at the start of last year, the data showed.
Iran's surging tanker exports weren't the only indicator of plentiful supplies.
US energy companies last week added oil rigs for a tenth week in a row, extending a recovery in activity into an eighth month as crude prices remained at levels at which many drillers can operate profitably.
"The next leg up in prices probably won't occur until the traders see evidence that production levels are falling. In the meantime, rising US drilling activity and output is likely to keep prices in check," ANZ bank said on Monday.
Drillers added four oil rigs in the week to Jan. 6, bringing the total count to 529, the most since December 2015, energy services firm Baker Hughes Inc said on Friday.
As a result of the increased drilling, US oil output has risen by over 4 percent from its 2016 low to almost 8.8 million barrels per day, although production remains 8.74 percent below its 2015 peak.
In physical markets, Iraq raised its February official selling price (OSP) for Basra Light crude to Asia by $0.50 to minus $0.90 a barrel against the average of Oman/Dubai quotes from the previous month, the State Oil Marketing Organization (SOMO) said on Monday.
