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* U.S. crude stocks rise to 466.4 mln barrels - API
* Crisis in Venezuela seen as risk to oil supply
* U.S. ends all waivers on Iran sanctions
* U.S. oil output, exports are rising: https://tmsnrt.rs/2ULQi5F (Updates prices, adds comment)
LONDON, May 1 (Reuters) - Oil prices were largely steady on Wednesday as an intensifying crisis in Venezuela along with tightened U.S. sanctions on Iran partly offset the impact of an unexpected rise in U.S. crude inventories.
Brent crude oil futures were at $72.14 per barrel at 1111 GMT, up 8 cents or 0.11 percent from their last close.
U.S. crude futures were down 28 cents or 0.44 percent at $63.63 per barrel.
Trading was thin as May 1 is a holiday in many markets.
U.S. crude stocks rose by 6.8 million barrels to 466.4 million barrels in the week to April 26, the American Petroleum Institute (API), an industry group, said on Tuesday.
The figure far outstripped analysts' expectations of an increase of just 1.5 million barrels.
Markets also keenly watched Venezuela, where opposition leader Juan Guaido called for an uprising against President Nicolas Maduro. Many observers fear this could lead to escalating violence and further disruptions to crude supply.
The unrest adds to a range of fluid geopolitical factors which have been affecting oil prices in recent months.
"There have been wild cards aplenty for the oil markets. The seemingly perennial U.S.-China trade spat, the extent of Venezuela's supply woes and the Iran factor are just some", PVM Oil Associates strategist Stephen Brennock said.
"Yet these are shaking off their wildcard status and instead are transitioning into known-knowns", Brennock added, citing widespread hopes that the two largest economies will soon resolve their dispute and a view that U.S. sanctions on Iran and Venezuela were "largely baked into prices".
Oil markets have already tightened this year due to supply cuts led by the Organization of the Petroleum Exporting Countries (OPEC) as well as the sanctions on Caracas and Tehran.
Washington is set to revoke waivers for select countries to import Iranian oil on Wednesday and says it aims to drive down Iran's crude exports to zero, but it remains unclear whether Iran's top oil customer China will comply.
OPEC meets in June to discuss production policy. While Washington has demanded the group increase output to make up for the shortfall from Iran, OPEC's de facto leader Saudi Arabia said on Tuesday it had no immediate plan to do so.
"Recent comments from (Saudi Energy Minister Khalid) al-Falih confirm our view that the kingdom will respond cautiously with other oil producers and not pre-emptively ramp up production," said Giovanni Staunovo, analyst at UBS in Zurich.
(Additional reporting by Henning Gloystein; Editing by Dale Hudson and Emelia Sithole-Matarise)