The Big Three U.S. auto makers on Tuesday reported significant increases in monthly sales in December, raising hopes that the industry is staging a sustained comeback.

General Motors (NYSE: GM) reported a 16% jump in December sales for the car maker’s four remaining brands compared with a year ago.

GM said it sold a total of 223,932 cars last month.

The gain was driven by an uptick in retail sales, which were 27% higher than a year ago, according to a statement released by the company.

For all of 2010, total sales for GM's four brands increased 21% to 2,202,927, while retail sales rose 16% for the year.

GM said its four brands sold 118,435 more vehicles in 2010 than the company did with eight brands in 2009.

"Our sales this year reflect the impact of GM's new business model. The consistency of results that we achieved demonstrates the focus on our brands, dealers and customers, and how we compete aggressively for every sale, every day," Don Johnson, GM’s vice president of U.S. sales said in the statement.

GM shed four brands as part of its government-orchestrated bankruptcy in the summer of 2009. Since scaling down its operations, the company has dramatically reduced its costs and debt load.

GM’s stock is up about 15% since completing an initial public offering of its stock in November.

Ford’s (NYSE: F) December retail sales increased 17% versus a year ago.

Among its brands, Ford retail sales were up 20% and Lincoln was up 3%. Mercury retail sales were down 29%, which the company said was consistent with its plan to discontinue the brand by the end of 2010.

Car retail sales increased 26% due to record monthly sales for the new Ford Fiesta subcompact and higher retail sales for the Ford Focus.

"With our balanced line of high-quality, fuel-efficient products, we have a solid foundation to deliver more sales and improved results in 2011," Ken Czubay, Ford vice president for U.S. Marketing Sales and Service, said in a statement.

Ford was the only one of the Big Three U.S. car makers not to accept a government bailout during the worst stretch of the economic crisis two years ago. GM and Chrysler both received billions of dollars in taxpayer support.

Meanwhile, Chrysler Group LLC reported U.S. sales of 100,702 in December, up 16% from a year earlier. For all of 2010, Chrysler said sales rose 17% to 1,085,211 vehicles from 2009.