CAPE TOWN, Feb 6 (Reuters) - Botswana's state diamond company resumed diamond auctions in January, its managing director said on Tuesday, after a two-month halt last year as the industry as a whole tackled a glut of inventory.

Demand for mined diamonds has sagged under the pressure of high interest rates in the United States, home to 55% of global consumption, China's sluggish recovery from the pandemic and competition from lab-grown gems.

The impact has been especially damaging in Botswana whose economy relies heavily on diamond sales.

The state's Okavango Diamond Company (ODC) held a gem auction in January and plans another this month as the market shows signs of improvement, Mmetla Masire, the company's managing director, told Reuters.

ODC, normally holds 10 auctions a year, but its last two in November and December were halted after only around 30% of the diamonds on offer found buyers, Masire said.

The company has started to reduce its inventories, but it is still unclear how robust demand is, Masire said. At the January auction, about 70% of the stones ODC had on offer were sold.

The ODC sells a share of the gems it is allocated from Debswana Diamond Company, Botswana's joint mining venture with Anglo American unit De Beers, on behalf of the government.

Its share of rough stones from Debswana will rise to 50% over the next decade from 25% last year after Botswana reached a new sales deal with De Beers in 2023.

Anglo CEO Duncan Wanblad told Reuters on Monday the company saw small signs of recovery in the diamond market.

"We can't say the market is as it was before. We will only possibly know about April how strong the recovery is," Wanblad said.

India, which cuts and polishes about 90% of the world's rough diamonds, asked global miners last year to stop selling to it as it sought to manage accumulated stocks. (Reporting by Felix Njini and Veronic Brown; editing by Barbara Lewis)