* Tensions mount over disappearance of Saudi journalist
* Stock markets falls again Monday, weighing on oil
* IEA cuts forecasts for oil consumption and demand for OPEC crude (Updates prices, market activity, adds commentary; changes byline, dateline, previous LONDON)
By Stephanie Kelly
NEW YORK, Oct 15 (Reuters) - Oil prices steadied on Monday, supported by geopolitical tension over the disappearance of a Saudi journalist, which has stoked worries about supplies from the world's top crude exporter, but weighed by a falling equities market and concern over long-term demand outlook.
Brent crude futures rose 33 cents to $80.76 a barrel by 11:26 a.m. EDT (1526 GMT). U.S. West Texas Intermediate (WTI) crude futures rose 27 cents to $71.61 a barrel.
Last week, both contracts fell by more than 4 percent as U.S. stock markets tumbled.
U.S. stock markets fell broadly on Monday, weighing on crude. Oil futures at times track with equity markets.
However, rising geopolitical tension between the U.S., the world's top oil consumer, and Saudi Arabia, one of the biggest oil producers supported prices on Monday.
Riyadh has been under pressure since journalist Jamal Khashoggi, a critic of the kingdom and a U.S. resident, disappeared on Oct. 2 after visiting the Saudi consulate in Istanbul.
U.S. President Donald Trump threatened "severe punishment" if it is found that Khashoggi was killed in the consulate.
Saudi Arabia said it would retaliate to any action against it over the Khashoggi case, state news agency SPA reported on Sunday, quoting an official source. This comes at a critical time for global oil markets, which are bracing for U.S. sanctions against Iran due to come into force Nov. 4.
The United States is still aiming to cut Iran's oil sales to zero, Washington's special envoy for Iran said on Monday.
Other producers are aiming to boost production amid falling Iranian exports, with Iraq planning to increase oil exports from its southern ports to 4 millions barrels per day (bpd) in the first quarter of 2019.
"If the Saudis don't come to the rescue when the Iranian sanctions kick in, you're really going to be short this market. It's going to be a very undersupplied market. That was the fear that was initially driving prices higher," said Phil Flynn, an analyst at Price Futures Group in Chicago.
However, some risk premium was taken out of the market when Trump on Monday raised the possibility that "rogue killers" could have been responsible for Khashoggi's disappearance.
Also exerting downward pressure on prices, Friday's monthly report from the International Energy Agency said the market looked "adequately supplied for now" and cut its forecasts for world oil demand growth this year and next.
OPEC, Russia and other oil producers, such as U.S. shale companies, had increased production sharply since May, the IEA said, raising world crude output by 1.4 million bpd.
The secretary general of the Organization of the Petroleum Exporting Countries last week said that the group saw the oil market as well supplied and that it was wary of creating a glut next year. (Reporting by Stephanie Kelly in New York, Christopher Johnson in London and Meng Meng and Aizhu Chen in Beijing; Editing by Marguerita Choy)