* Trump fires hardline adviser Bolton
* New Saudi energy minister: OPEC+ alliance staying for long term
* POLL-U.S. crude inventories likely fell for fourth straight week
* Coming Up: API energy data at 4:30 p.m. (2130 GMT)
* Graphic on U.S. inventories: tmsnrt.rs/2y7dfqh (Updates prices, adds Bolton firing, EIA monthly report and comments)
By Laila Kearney
NEW YORK, Sept 10 (Reuters) - Oil prices steadied after falling sharply on Tuesday on news that U.S. President Donald Trump fired national security adviser John Bolton, the chief architect of Trump's strident stance against Iran.
The market was, however, still supported by expectations of continued output cuts by the Organization of the Petroleum Exporting Countries and its allies after assurances by Saudi Arabia's new energy minister.
Brent slid 7 cents to $62.52 a barrel by 2:21 p.m. EDT (1821 GMT), while U.S. West Texas Intermediate (WTI) futures fell 26 cents to $57.59 a barrel.
Trump abruptly fired Bolton amid disagreements with his hardline aide over how to handle foreign policy challenges such as North Korea, Iran, Afghanistan and Russia.
Iran's crude oil exports were slashed by more than 80% due to re-imposed sanctions by the United States after Trump exited last year Iran's 2015 nuclear deal with world powers. In May, Washington ended sanction waivers given to importers of Iranian oil, aiming to cut Tehran's exports to zero.
"It implies that there is at least a slight possibility that there could be some kind of break in the oil sanction waiver situation," said Bob Yawger, director of energy futures at Mizuho.
Yawger added that the market was further pressured by the U.S. Energy Information Administrations (EIA) lowering its spot crude oil price forecasts.
In its latest monthly Short Term Energy Outlook, the EIA reduced its forecast for spot West Texas Intermediate crude prices for 2019 to an average of $56.31 per barrel from $57.87 in its August report.
The EIA also reduced its forecast for spot Brent prices for 2019 to an average of $63.39 per barrel from $65.15.
Oil prices were higher earlier in the session after Prince Abdulaziz bin Salman, Saudi Arabia's new energy minister and a longtime member of the Saudi delegation to OPEC and its allies, said the kingdom's policy would not change and a global deal to cut oil production by 1.2 million barrels per day would be maintained.
He added that the so-called OPEC+ alliance, which includes non-OPEC producers such as Russia, would be in place for the long term.
The OPEC+ joint ministerial monitoring committee (JMMC), which reports on compliance with the cuts, is due to meet on Thursday in Abu Dhabi.
Goldman Sachs lowered its forecast on 2019 oil demand growth to 1 million bpd, down 100,000 bpd, but left its 2020 demand growth estimate broadly unchanged at 1.4 million bpd.
"Our oil supply-demand outlook for 2020 calls for additional OPEC production cuts to keep inventories near normal," Goldman analysts wrote in a note.
In the United States, crude stockpiles were forecast to have fallen for a fourth consecutive week, dropping 2.7 million barrels last week, a Reuters poll showed.
Additional reporting by Noah Browning, Scott DiSavino and Aaron Sheldrick; Editing by Marguerita Choy and Tom Brown