NEW YORK, Jan 6 (Reuters) - Benchmark U.S. crude futures suggest oil supplies will remain tight early in the new year, even as the Omicron coronavirus variant has raised worries that the pandemic, which has dampened fuel consumption, is not going away anytime soon. The tighter market could lead to higher prices for energy consumers, as OPEC+ struggles to raise production while U.S. drillers restrain output because of investor demands. Fuel consumption has roared back from pandemic lows, creating relatively steady drawdowns in oil inventories. Oil contracts marked for delivery in a few months are much pricier than those much further down the road, a signal of near-term rising demand. A barrel of oil for delivery in June is selling at a $4.10 premium to a barrel for delivery in December, the highest since Nov. 2. For delivery in December, barrels are selling at an about $5.70 premium to December 2023, the steepest premium since Nov. 3. "Supplies are getting somewhat tight," said John Kilduff, partner at Again Capital LLC in New York. "We"re back to pricing in those relative tight supplies here as we go forward over the next few weeks." Crude inventories in the United States, the world"s top consumer, have fallen for six consecutive weeks by the end of the year to 417.9 million barrels, their lowest since September, according to the Energy Information Administration. Many analysts do not foresee a notable increase in production soon. The Organization of the Petroleum Exporting Countries in December undershot its planned increase in production, a Reuters survey found on Thursday. read more OPEC and its allies, a group known as OPEC+, are gradually relaxing 2020"s output cuts as demand recovers. But many smaller producers cannot raise supply and others have been wary of pumping too much in case of renewed COVID-19 setbacks. U.S. production, meanwhile, remains far below the 13 million barrels per day record hit in late 2019 that made the country the world"s top producer, with the four-week average around 11.7 million bpd, EIA data showed. Though the oil futures market halted its rally in late November and some of December with the spread of the Omicron variant, prices are roaring back again. "The curve is telling you that the market needs your barrels now," said John Saucer, vice president and head of crude oil markets at Mobius Risk Group. "It was really tight in November, we had a bit of a pause, but that tightness is coming right back." Meanwhile, the four-week average for U.S. implied fuel demand rose to 21.4 million bpd in the week to Dec. 24, the highest since 2019, barring one week in September this year, EIA data showed. "Demand has exceeded everyone"s expectations," Saucer said.