The price and range of the five-seater should make the vehicle appeal to new types of customers and could boost interest in other electric vehicles.
Chief executive Elon Musk said his goal was to produce about 500,000 vehicles a year once production is at full speed.
Within a day of the launch, Mr Musk tweeted that 180,000 vehicles had been pre-ordered.
He added that, if the average price tag ended up at $42,000 (£29,500), this would equate to $7.5bn in one day.
The California-based company needs the vehicle to prove popular if it is to stay in business, though pre-orders of the Model 3 will not necessarily all translate to actual sales when the car is released.
The first deliveries of the vehicle are scheduled to start in late 2017, and it can be ordered in advance in dozens of countries, including the UK, Ireland, Brazil, India, China and New Zealand.
The basic model will start at $35,000 (£24,423) and have a range of at least 215 miles (346km) per charge.
Tesla delivered 50,580 vehicles last year. Most of those were its Model S saloon,which overtook Nissan’s Leaf to become the world’s best selling pure-electric vehicle.
But the firm still posted a net loss of $889m (£620m) for 2015, partly because it spent $718m on research and development over the period.
It left Tesla with cash reserves of $1.2bn, down from $1.9bn a year earlier.
“For a long time there had been questions about the long term viability of Tesla,” commented Jessica Caldwell, an industry analyst at the car research site Edmunds.
“With niche products like the Model S and the Model X, it hasn’t been hitting any sales targets that would sustain its business.
“So, launching what it hopes will be high-volume vehicle is going to show if it can become a fully-fledged auto company that will succeed in the long-term rather than one that pumps out a few cool cars and then goes bust, as we’ve seen happen with other electric car start-ups such as Fisker.”
Other details provided about the Model 3 included:
- The base model will accelerate from zero to 60mph (97km/h) in less than six seconds, other models will go faster
- It will include the “autopilot” safety features found in existing models, which allow the cars to steer themselves and avoid collisions
- It will support “supercharging” as standard, allowing the cars to recharge more quickly at special power stations. Tesla aims to double the number of places offering supercharging to about 7,200 worldwide by the end of 2017
- It provides storage room at the front and rear of the vehicle
Mr Musk added that the car should feel more spacious to passengers than similar-sized petrol-based cars because of design decisions Tesla could make by not using a combustion engine.
“You are sitting a little further forward,” he explained. “That’s what gives you the legroom to have five adults.”
“And the rear roof area is actually one continuous pane of glass.
“The reason that that’s great is because it gives you an amazing feeling of openness. So, it has by far the best roominess of any car of this size.”
In scenes more commonly associated with smartphone launches than those of vehicles, hundreds of people queued outside Tesla stores in the US to try to secure one of the first Model 3s.
They had to pay a $1,000 deposit to reserve the car before they had even seen it. The company also began taking online orders an hour before its press event had begun.
At the end of his presentation, Mr Musk said that Tesla had already received more than 115,000 orders.
The move should help the firm head off competition from other forthcoming similarly-priced electric cars that will become available first, including General Motors’ Chevy Bolt and BYD’s Qin EV300.
Part of the incentive to commit early is that a $7,500 tax credit offered to US buyers is set to be pulled once the company has sold 200,000 vehicles in the country.
“If you look at the US auto market, the average purchase price is about $33,000, which is close to what the target for the Model 3 is,” said Ms Caldwell.
“So, it becomes less of that pie-in-the-sky dream car and something that the average person can actually afford.
“That’s why people are excited about it in non-traditional Tesla markets – places outside of San Francisco Bay and Los Angeles – and why we saw lines in places like Houston and Arizona.”
Analysis: Dave Lee, North America technology reporter
You could call it Tesla’s Kickstarter campaign.
At tonight’s event, computers were set up for people to throw their cash into Elon Musk’s coffers to fund the Model 3 project.
One of them was 16-year-old Adam Metcalf, there with his father, who had saved up “all the allowance I’ve ever had” to put down a deposit for what will be his first car.
Adam hopes to get into the driver seat when it launches at the end of next year. He’ll need a serious allowance, mind, even if government subsidies eat into the $35,000 headline price.
If Adam can’t quite stretch that far, his deposit will be refunded. Which makes you wonder – how many of the 115,000 pre-orders (and counting) will turn into actual sales? As I say, it’s like the crowdfunded pitches on Kickstarter. You don’t quite know if the end product will be the success promised at launch.
No doubt about it, Musk needs to sell a lot of the Model 3.
While lining up to get in, I spoke to the managing director of a major European investment bank, who didn’t want to be named.
He said the eccentric, rocket-making Musk remains a popular figure, of course, but that patience is quickly running out. Investors are demanding profitability this year – Musk says he can deliver.