BEIJING, April 21 (Reuters) - Tesla has cut prices in China by nearly $2,000 across its line-up in China, in line with its price cuts in the United States, as it grapples with falling sales and an intensifying price war for electric vehicles (EVs).

Elon Musk's EV maker cut the starting price of the revamped Model 3 by 14,000 yuan ($1,930) to 231,900 yuan ($32,000) in China, its official website showed on Sunday.

Tesla made similar cuts to the Model Y starting price, now 249,900 yuan, the regular version of the Model S to 684,900 yuan and the Model S Plaid to 814,900 yuan. The regular Model X now costs 724,900 yuan and its plaid variant 824,900 yuan.

The carmaker cut U.S. prices of its Model Y, Model X and Model S vehicles by $2,000 each on Friday. On Saturday it slashed the price of its Full Self-Driving driver assistant software to $8,000 from $12,000 in the United States.

Tesla reported this month that its global vehicle deliveries in the first quarter fell for the first time in nearly four years, as price cuts failed to stir demand.

The EV maker has been slow to refresh its ageing models as high interest rates have sapped consumer appetite for big-ticket items, while rivals in China, the world's largest auto market, are rolling out cheaper models.

Musk postponed a planned trip this weekend to India, where he was to have met Prime Minister Narendra Modi, citing obligations at Tesla.

($1 = 7.2403 Chinese yuan renminbi)

(Reporting by Ethan Wang, Bernard Orr and Hyunjoo Jin; Editing by Michael Perry and William Mallard)