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* UK says COVID surge 'extremely difficult'; Omicron grips Europe

* OPEC+ produces below target in November as compliance rises

* U.S. crude inventories expected to fall 4th straight week - poll

* Coming up: API inventory data due at 2130 GMT

SINGAPORE, Dec 21 (Reuters) - Oil prices edged higher on Tuesday, though investors remained worried about the rapid spread of the Omicron coronavirus variant globally, prompting countries to consider more restrictions potentially denting fuel demand.

Brent crude futures increased by 9 cents, or 0.1%, to $71.61 a barrel by 0105 GMT, while U.S. West Texas Intermediate crude futures rose by 23 cents, or 0.3%, to $68.84 a barrel.

"It also looks increasingly likely that the UK will reimpose restrictions sometime after Boxing Day (Dec 26), with daily cases moving to record highs," analysts from JBC Energy wrote in a note on Tuesday.

British Prime Minister Boris Johnson said on Monday he would tighten coronavirus curbs to slow the spread of the Omicron variant if needed, after the Netherlands began a fourth lockdown and other European nations considered Christmas restrictions.

Omicron infections are multiplying rapidly across Europe and the United States, doubling every two or three days in London and elsewhere and taking a heavy toll on financial markets, which fear the impact on the global economic recovery.

Still, Moderna Inc said on Monday that a booster dose of its COVID-19 vaccine appeared to be protective against the fast-spreading Omicron variant of the coronavirus in laboratory testing, providing some hope to investors.

On the supply front, OPEC+ compliance with oil production cuts rose to 117% in November from 116% a month earlier, two sources from the group told Reuters, indicating production levels remain well below agreed targets.

In the United States, crude oil inventories were expected to have fallen for a fourth consecutive week, while distillate and gasoline stockpiles likely rose last week, a preliminary Reuters poll showed on Monday.

The poll was conducted ahead of reports from the American Petroleum Institute, an industry group, due on Tuesday, and the EIA, the statistical arm of the U.S. Department of Energy, due on Wednesday.