* U.S. oil rig count drops to lowest since June
* Iraq supplies cut amid fighting between govt forces, Kurds
* Iraq, Saudi Arabia hail OPEC cooperation (Updates throughout, changes dateline, previous SINGAPORE)
AMSTERDAM, Oct 23 (Reuters) - Oil prices largely held on to last week's gains on Monday, supported by supply disruptions in Iraq and a drop in U.S. drilling.
However, the reduction in drilling rigs in the United States could be temporary, analysts said, as activity had been restrained by hurricane threats.
The number of U.S. rigs drilling for new oil fell by seven to 736 in the week to Oct. 20, the lowest level since June, energy services firm Baker Hughes said on Friday. <RIG-OL-USA-BHI>
Global benchmark Brent crude was trading at $57.56 a barrel at 0957 GMT, down 19 cents.
U.S. West Texas Intermediate (WTI) crude was up 2 cents at $51.86.
"The market is in a tug of war between short-term bullish drivers which are very true, very visible and very strong versus real concerns for the oil market balance for 2018," said Bjarne Schieldrop, chief commodities analyst at SEB Markets.
One bullish factor is supply disruptions in northern Iraq, where tensions have been running high since the Kurdistan region's vote in favour of independence last month.
As of Sunday, oil exports from Iraq's Kurdistan via the Turkish Mediterranean port of Ceyhan were still flowing at sharply reduced rates between 200,000 and 250,000 barrels per day, two shipping sources said. Flows had increased slightly to 255,000 bpd by Monday, one source said.
Typically, the pipeline transports around 600,000 bpd.
Iraqi Oil Minister Jabar al-Luaibi said on Saturday oil exports were increasing from the southern Basra region by 200,000 bpd to make up for a shortfall from the northern Kirkuk fields.
In a landmark visit to Iraq, Saudi Arabia's Energy Minister Khalid al-Falih praised the two countries' collaboration within the Organization of the Petroleum Exporting Countries to cut production in an effort to prop up prices.
Iraq said the two countries would continue to cooperate in implementing decisions by oil-exporting countries.
The remarks come just over a month ahead of the group's next scheduled meeting, at which the oil exporters are expected to announce further decisions on their production-curbing deal.
"The market looks considerably different now than it did just a few months ago and signals coming from the organization itself and member countries continue to be constructive for prices," analysts at JBC Energy wrote.
The crude oil volatility index, which measures market expectations for 30-day price volatility, fell to levels similar to those seen in 2014 last Friday.
(Additional reporting by Henning Gloystein in Singapore; Editing by Dale Hudson)