Plans for the tax, which was to have entered into force in 2018, were halted after a budget compromise was reached between the right-wing government and its centre-right allies, which they presented on Wednesday evening.
"It's a happy day," Norwegian Electric Vehicle Association secretary general Christina Bu said.
Norway, a large oil and gas producer, has introduced numerous incentives to encourage the purchase of electric cars. Buyers pay almost no tax, making the sale price very competitive.
As a result, sales of zero emission vehicles account for more than 20 percent of new car registrations, a market share unparalleled in the world.
In its budget bill, the government had in October proposed to abolish one of the tax exemptions granted to electric cars weighing more than two tonnes.
The proposal was immediately dubbed the "Tesla tax" because it would primarily have affected the high-end models made by the American manufacturer, hiking the price of a new Tesla X by about 70,000 kroner (7,500 euros).
The Liberal party, a key ally of the minority government, was opposed to the tax, arguing that a 2015 accord had called for the tax exemptions to remain in place until 2020.
Norway has set an ambitious target of ending the sale of new cars with combustion engines as early as 2025.
The Scandinavian country is powered almost entirely by green hydro power, and must make an effort in its transport sector if it wants to meet its greenhouse gas emissions reduction goals.
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