FRANKFURT, Germany (AP) -- Luxury carmaker BMW AG has posted record sales for 2013, keeping its No. 1 spot in the market for high-priced cars against its German competitors Audi and Mercedes.

The Munich-based company said Monday it sold 1.66 million vehicles under the BMW brand, 7.5 percent more than last year.

The figure was boosted by strong sales of the brand's mainstay 3-series sedan and X1 small SUV as well as by rising demand in China and the United States. Sales of the 3-series rose 23 percent.

Volkswagen AG's Audi division last week reported sales of 1.57 million last year and Daimler AG's Mercedes-Benz brand came in at 1.46 million.

The three carmakers are pillars of Germany's export-focused economy and have reaped fat earnings selling luxury cars and SUVs -- which earn higher profits per vehicle than mass-market vehicles -- in the United States and in emerging markets, led by China.

The competition among the three heats up Monday at the start of the North American International Auto Show in Detroit, where Mercedes is introducing a new version of its C-Class that will compete with the BMW 3-series.

BMW is showing off its new 2-series small sports coupe.