Australian-based Tesla spokesman Heath Walker said in a statement he was unable to release figures on how many pre-orders had been made from New Zealand alone and said no other plans from the company had been confirmed.
Since the unveiling on Friday, Musk said orders for the Model 3 were running at double what had been expected.
If Model 3 orders hit 500,000 it would require another factory in Europe to meet demand, he said in a tweet.
Tesla vehicles brought to New Zealand through Australian dealerships are shipped back to Australia for maintenance work.
Walker said this was standard and all Tesla buyers were informed about this prior to purchase.
Musk hinted at New Zealand-based dealerships, saying by the end of 2017 the number of Tesla locations where people can buy or service cars will more than double to 441 worldwide.
Tesla has a history of missing deadlines for its vehicles to hit the market, but Musk said last week that he feels "fairly confident" that the Model 3 will come out next year.
Customers put down $1470 (US$1,000) to order the cars, which start at $50,000 (US$35,000) and have a range of 215 miles per charge.
While production for the Tesla Model 3 to New Zealand does not start until 2018, Musk said pre-ordering a vehicle makes a big difference in terms of priority.
The number of Model 3 orders is unprecedented when compared with electric car sales worldwide, especially for just a few days after opening. Nissan, which says its Leaf is the top-selling electric car in the world, has sold 211,000 of them since distribution began in late 2010. Tesla has sold a total of 110,000 electric cars since it started doing business in 2008.
Musk told people during weekend Twitter sessions that he expected one-quarter to one-half the number of orders. "No one at Tesla thought it would be this high before part two of the unveil" which will take place closer to when production starts, he wrote.
At 276,000 orders, Musk's company gets a cash infusion of $276 million from deposits and an order book valued at $11.6 billion based on Musk's estimated average Model 3 cost of $42,000 with options.
Musk, who hasn't given out all details of the Model 3 yet, says the car will be rear-wheel-drive with optional all-wheel-drive, and its steering controls will feel like a spaceship.
READ MORE:
• New Zealand to get Tesla Model 3
• Affordable Model 3 is Tesla's biggest test
Tesla plans to have a presence in India before Model 3 production starts, and its high-speed charging system and service will cover all of Italy later this year, Musk says.
The Model 3 is less than half the cost of Tesla's previous models, and its range is about double what drivers get from current competitors in its price range, such as the Nissan Leaf and BMW i3. It also faces competition from General Motors, which is set to start selling the Chevrolet Bolt electric car at the end of this year with a similar price tag and a 200-mile range.
The orders boosted Tesla shares even though broader stock markets were slightly lower on Monday. Shares rose 4 per cent to close at $246.99, earlier in the day peaking at $252.12, their highest intraday price since early October.
The stock slipped 2.4 per cent in after-hours trading after the company announced its first-quarter deliveries.
- with additional reporting from AP.
