The car was shown off at an event in California by chief executive Elon Musk as the company continues to face serious questions over its manufacturing capacity after failing to meet demand for its Model 3.
He told an audience comprising staff, customers and reporters that it would remain the priority, with the first Model Y not due to be completed until autumn next year.
“Because of extreme challenges with the Model 3 production, we have to basically allocate all resources to Model 3 production, because otherwise we’re going to die,” he said.
Tesla has announced thousands of job cuts and cost-cutting measures in recent months as it moves to bring down the cost of the basic Model 3 – hitting $35,000 from $43,000 a couple of weeks ago.
Mr Musk’s promises to investors on reaching key targets were seen as driving him to the point of exhaustion in 2018 when he also fell foul of stock market rules through a series of tweets over the possibility of taking Tesla private.
That cost the firm a $40m settlement.
US car market analysts saw the Model Y as a good move due to the growing popularity of SUVs worldwide.
The all-electric factor was, they suggested, a bonus as the authorities in China and Europe in particular demand low emission vehicles.
Mr Musk said of the Model Y: “It has the functionality of an SUV, but it will ride like a sports car.
“This thing will be really tight on corners and we expect it will be the safest midsize SUV in the world by far.”
The Model Y seats seven and has a panoramic glass roof and a 15in (38cm) touchscreen interface for accessing all the car’s controls.
The all-electric, mid-size SUV will start at $39,000 for the standard range version, which the company said can go 230 miles on a single charge.
The long-range model, which starts at $47,000, has a range of up to 300 miles – less range than the Model 3.
A dual-motor, all-wheel drive version, would start at $51,000 while the performance version of the car, which boasts acceleration of 0-60 mph in as little as 3.5 seconds, would begin at $60,000.
Gartner analyst Mike Ramsey told the AP news agency to expect a rocky road for the Model Y.
“This could be Tesla’s most profitable vehicle, with the giant asterisk that the company doesn’t do some of the dumb things it has in the past.”
He added: “Until Elon is gone, Tesla is going to be a crazy company that occasionally makes breathtaking products.”