Jan. 1 is the official start of the deal agreed by the Organization of Petroleum Exporting Countries (OPEC) and several non-OPEC producers to lower production by almost 1.8 million barrels per day (bpd).

Brent crude was up 17 cents at $55.33 a barrel at 1340 GMT. The global benchmark reached $57.89 on Dec. 12, the highest since July 2015. US crude gained 30 cents to $53.32.

Trading was thin on Tuesday, with less than one-third of the usual volume in futures contracts in West Texas Intermediate crude oil.

"Some of the doubts (in OPEC) people are showing are going to have to be put to rest," said Phil Flynn, analyst at Price Futures Group in Chicago. "There is a strong possibility that we are going to rally into the end of the year."

The members of an OPEC and non-OPEC committee formed to monitor the market may meet on Jan. 13, two sources said. Oil rallied further after news of the meeting, which may give an early indication of compliance with the deal.

"From January, we will start to have a better idea about the level of OPEC production," said Olivier Jakob, oil analyst at Petromatrix.

"To go above $60 is going to be difficult. We are already close to the top rather than the bottom of the range right now," he said."

Russian oil producer Gazprom Neft said on Tuesday it planned to increase oil production by 4.5 to 5 percent next year, less than intended before Russia joined the supply cut deal.

Major OPEC members such as Saudi Arabia and Iraq have informed customers of lower supplies. But Libya and Nigeria - which are exempt from reductions because conflict has curbed their output - have been increasing production.

Products markets outpaced crude on Tuesday, as the price of reformulated blendstock gasoline gained 2.4 percent to $1.6652 a gallon, while heating oil gained 2.9 percent to trade at $1.71 a gallon. Those contracts expire Friday; options on those contracts are expiring Tuesday.

Venezuela said on Tuesday it would cut 95,000 barrels-per-day of oil production in the New Year.

"Without prejudicing its international contractual obligations, from Jan. 1, 2017, (state oil company) PDVSA and/or its subsidiaries will implement a reduction in the volumes of its main crude sale contracts, all in conformity with existing terms and conditions," the Energy Ministry said.

-Reuters