BOGOTA, Dec 19 (Reuters) - Colombia's central bank cut the benchmark interest rate by 25 basis points to 13% on Tuesday to mark its first cut in more than three years, as policymakers sought to boost the ailing economy despite continued inflation pressures on some sectors.

The decision was backed by five policymakers, while two voted to hold borrowing costs. The reduction marks the first cut to the rate since September 2020.

The bank also lowered its growth projection for 2023 to 1%, down from a previous estimate of 1.2%.

Though fuel and energy prices have continued to increase, "inflation continued the downward path it has maintained over the last eight months and in November stood at 10.15%," the board said in a statement.

The November figure is still far above the bank's long-term target of 3%.

Food prices notched important reductions, the statement added, and inflation expectations for next year are mixed.

But economic growth is suffering, the board said.

"What is important is the message in a scenario where there is clear economic deceleration and we still have worrying symptoms," said Finance Minister Ricardo Bonilla, who represents the government on the board.

The meeting comes a day after the statistics agency said gross domestic product contracted 0.41% year-on-year in October, the third consecutive monthly contraction, and amid uncertainty over how much the monthly minimum wage will be increased for 2024.

"Economic activity continues decelerating," said board chief Leonardo Villar.

Analysts have said both fuel prices and a hike in the minimum wage could influence the inflation level next year.

"The board of directors calls for caution in adjusting the minimum wage, so that its increase does not significantly exceed the annual variation of the consumer price index in 2023," the statement added.

Unions and business groups, accompanied by the labor ministry, are still debating the rise.

Six of 20 analysts surveyed by Reuters last week said the bank would cut the rate to 13%, while five backed a 50 basis points trim and nine predicted a hold at 13.25%, which had been its highest point in 24 years.

According to the Reuters survey, the interest rate will stand at 8% at the end of next year and then fall further to 5.5% in 2025.

(Reporting by Nelson Bocanegra and Carlos Vargas, Writing by Julia Symmes Cobb, editing by Deepa Babington)