* Iraqi forces take Kurdish-held oil city of Kirkuk
* U.S.-Iran tension helps raise global risk premium for oil
* BoAML sees sizeable deficit on strong demand, tight supply (Updates throughout, changes dateline, previous SINGAPORE)
LONDON, Oct 17 (Reuters) - Oil prices steadied on Tuesday, holding on to gains made as fighting between Iraqi and Kurdish forces threatened supplies from northern Iraq while political tension rose between the United States and Iran.
After months of rangebound trading during which OPEC-led supply cuts supported crude values but rising U.S. output capped markets, prices have moved up significantly this month.
Brent crude oil was 5 cents higher at $57.87 a barrel by 0730 GMT, up almost a third from its mid-year levels. U.S. West Texas Intermediate (WTI) crude was unchanged at $51.87.
Iraqi government forces captured the Kurdish-held oil city of Kirkuk on Monday, responding to a Kurdish independence referendum. There were unconfirmed reports that Kurdish forces had shut around 350,000 barrels per day (bpd) of oil production from major fields.
"In the case of Kurdistan, the 500,000 bpd Kirkuk oilfield cluster is at risk," Goldman Sachs said in a note to clients.
Tension between the United States and Iran is rising, also raising the global risk premium for oil.
U.S. President Donald Trump on Friday refused to certify Iran's compliance over a nuclear deal, leaving Congress 60 days to decide further action against Tehran.
"If there (were new sanctions), we expect that several hundred thousand barrels of Iranian exports would be immediately at risk," Goldman said.
During the previous round of sanctions against Iran, around 1 million bpd of oil was cut from global markets.
"Oil and geopolitics are very much interlinked," Fatih Birol, executive director of the International Energy Agency, told Reuters on Tuesday. "Oil security remains a critical issue for all the countries."
With supply cuts led by the Organization of the Petroleum Exporting Countries tightening the market, analysts have been revising upward their oil price forecasts.
Birol said the rate of compliance by OPEC and its partners in their targeted cutting of around 1.8 million bpd between January this year and March 2018 was about 86 percent.
Bank of America Merrill Lynch said it was raising its oil price forecasts.
"We see Brent averaging $54 this quarter and $52.50 per barrel in 1H18, compared with our previous forecasts of $50 and $49.50 per barrel respectively. We also adjust WTI to average $49 this quarter, relative to our previous forecast of $47 per barrel."
Merrill Lynch said it expected a sizeable deficit in 2017 of 230,000 bpd, and that there was further upside potential to its outlook. (Additional reporting by Henning Gloystein in Singapore; Editing by Dale Hudson)