To help lower the price the firm plans to close showrooms and is switching to an online-only sales model.
The electric car company announced the Model 3 car in 2016 as an alternative to its luxury offerings.
However, as recently as September, the average selling price exceeded $50,000.
Closing physical stores will allow the firm to cut costs by about 5%, savings it is using to reduce prices across its line-up of vehicles, chief executive Elon Musk said.
He declined to say how many stores would close, or how many people will lose their jobs as a result of the move, but said making the change was necessary as Tesla works toward its bigger goal of making electric cars mainstream.
Tesla currently has 378 stores and service locations worldwide.
What is the Model 3?
The Model 3 electric car has a range of 220 miles, a top speed of 130 mph and 0-60mph acceleration of 5.6 seconds.
More than 400,000 customers signed up for the car when it was first announced, but production issues, higher prices and other delays caused troubles following its launch.
Over the last year, the firm has shrunk the Model 3 battery, tweaked its manufacturing process, and reduced costs in other ways to hit the lower price, while still protecting profit margins.
Fewer showrooms: How will that work?
Mr Musk said he was not worried that a shift to online-only sales would put off customers.
The firm already has a much smaller physical presence in the US than most other car companies.
In a blog post, Tesla said a test drive was not needed because you can return a car within seven days, or after driving 1,000 miles, and get a full refund.
“Quite literally, you could buy a Tesla, drive several hundred miles for a weekend road trip with friends and then return it for free,” the blog said.
The company is confident that will not happen often.
Tesla’s website said cars ordered now would be ready for delivery in two to four weeks’ time. However, customers with orders already in queue will get priority, which could delay some deliveries until June, Mr Musk said.
The lower-priced model is expected to be available for order in Europe and China in three to six months’ time.
Why is the Model 3 important?
Tesla has already announced thousands of job cuts since June, as it tries to balance its books after years of losses.
Strong sales of the Model 3 are critical to that effort.
The firm managed to scrape a profit in the final two quarters of 2018, but Mr Musk said it expected to post a loss for the first three months of this year.
“It has been insanely difficult,” Mr Musk said, referring to delivering on the $35,000 price promise.
Delivering a car for $35,000 – about the average cost of a new vehicle in the US – is a “potential game changer” for Tesla’s growth, said Daniel Ives, a managing director at Wedbush Securities.
“While there are still questions that need to be answered around logistics and delivery… we believe this strategic shift was the right move at the right time for Tesla,” he wrote in a note.
How self-driving is it?
Tesla is now offering two software packages; regular autopilot, at a cost of $3,000 (£2,270) which will allow for automatic steering on highways or full self-driving ($5,000) which takes over more functions, such as changing lanes, navigating junctions and taking exits.
According to chief executive, Elon Musk, the self-driving software will get an upgrade later this year which will allow it to navigate in more complex city environments.
Coinciding with the price drop, Tesla is also bringing back its “full self-driving” feature after it removed it in October, following criticism it was overstating the autonomy of its cars.
If you’ve ever wondered how those enormous Tesla stores in fancy shopping centres make money, well, they don’t.
At least, they don’t make enough money for Tesla to keep them all open if it also wants to be able to afford to produce a $35,000 car – a car its investors (and many customers) have been desperately waiting for since it was announced way back in March 2016.
The hope is that this is the car that brings a Tesla into the affordability zone for a whole new type of customer. It’s still an incredibly expensive car for almost all of us, but for a luxury electric vehicle this is new ground.
The Tesla brand, and its ramped up production capabilities, make it likely the cheap(er) Model 3 will turn out to be a popular proposition.
But Tesla’s admission it would not, as it had previously said, turn a profit this quarter, has spooked investors – as has admitting it needs to lay off workers and scale back its bricks-and-mortar presence in order to make good on a long-held promise is of concern.
Coupled with his SEC woes lingering overhead, Mr Musk hasn’t exactly lost his investors’ confidence, but he hasn’t exactly filled them with it either.