Audi's previous record for monthly sales was 150,300 vehicles sold in September 2013.
Audi's first-quarter deliveries also reached a new record, rising 12 percent to 412,850 cars and SUVs. It is the first time the company has sold more than 400,000 vehicles in the first three months of a year, Audi said, adding that its year-on-year sales have risen for 51 consecutive months.
"In March we achieved a double-best figure, completing the most successful first quarter in our company history with the strongest sales month ever," Luca de Meo, Audi’s sales chief, said in the statement.
Mercedes’ quarterly sales rose 15 percent to 374,276 vehicles last month, which was also a new all-time high for the automaker.
Another model giving Audi a boosted is the Q7. Sales of the premium large SUV rose 39 percent in March, while deliveries of the range-topping A8 upper-premium sedan jumped 49 percent.
Audi made gains in all its major markets last month, with deliveries in China rising 37 percent to 47,636 while U.S. sales rose 8 percent to 14,246. In Europe, Audi's sales increased 7 percent to 88,750. Audi's top European market was the UK, where sales rose 13 percent to 28,068, followed by Germany, where deliveries were up 10 percent to 27,226.