NEW YORK, Sept 5 (Reuters) - Near-term prices for oil traded on Tuesday at their steepest premium since November to later-dated prices after Saudi Arabia and Russia announced plans to extend voluntary oil supply cuts for three months.

Oil futures surged on the news, as investors weighed the announcement with recent large falls in U.S. crude inventories that point to tightening oil market fundamentals. Refiners are running hard to keep up keep up with strong fuel demand.

Changes in the calendar spreads reflected concern about tight near-term supplies.

Front-month Brent futures traded on Tuesday as much as $4.37 a barrel above prices in six months , the highest premium since November 2022.

For U.S. WTI futures, the spread between front-month and the six-month contract widened to as much as $4.88 a barrel on Tuesday, also the most since November.

The higher near-term prices encourage producers and traders to sell oil from storage to help meet short-term demand.

"Right now there's a disincentive to buying oil and storing it because it is only going to fall in value," said John Kilduff, partner at Again Capital.

"Things will likely get tighter and prices get higher as a result of the backwardation we're experiencing," Kilduff added, referring to the market structure in which spot prices are higher than prices in the future.

Saudi Arabia will extend its voluntary oil output cut of 1 million barrels per day (bpd) for another three months until the end of December 2023, state news agency SPA said on Tuesday, citing an energy ministry official.

Russia extended its voluntary decision to reduce its oil exports by 300,000 bpd to the end of this year, Deputy Prime Minister Alexander Novak said in a statement on Tuesday. The voluntary cuts are on top of the April cut agreed by several OPEC+ producers, which extends to the end of 2024.

In the week to Aug. 25, U.S. crude inventories fell by 10.6 million barrels to 422.9 million barrels, the lowest since December, Energy Information Administration data showed. The U.S. exported 4.5 million bpd of oil. (Reporting by Stephanie Kelly; Editing by Simon Webb and Timothy Gardner)