Tesla electric car sales in Europe plunged in the first three months of the year, industry data showed on Thursday, in a fresh blow to its boss Elon Musk who has been criticised for his work in US President Donald Trump's administration.

Sales of the sleek machines fell 45 percent to just over 36,000 units in the first quarter in the 27-nation bloc, the European Automobile Manufacturers' Association, or ACEA, said in a report.

They dropped by 36 percent just in March, suffering in both periods the biggest fall in sales of any of the major car groups tallied in the association's report, despite a growth in electric vehicle sales overall.

Tesla showrooms have been hit by vandalism, demonstrations and boycott calls in Europe and the United States in a backlash against public service cuts introduced by Musk in his role as a close adviser to Trump.

On Tuesday the company reported a 71-percent drop in first-quarter profits, signalling a hit to demand due to what it called "changing political sentiment".

It reported profits of US$409 million following a drop in sales, while revenues fell 9 percent to US$19.3 billion.

Musk promptly announced he would scale back his work for the Trump administration in May to focus on Tesla.

Trump's combative trade policies have raised concerns in the auto sector after he enacted 25-percent tariffs on cars imported into the United States to try to boost US manufacturing.

"Uncertainty in the automotive and energy markets continues to increase as rapidly evolving trade policy adversely impacts the global supply chain and cost structure of Tesla and our peers," Tesla said on Tuesday.

"This dynamic, along with changing political sentiment, could have a meaningful impact on demand for our products in the near-term."

Tesla pointed to tariffs as another headwind for the company and analysts have also cited a stale portfolio of vehicles as among the challenges facing the company.

But Tesla said it was on track to launch new vehicles "including more affordable models" in the first half.

Analysts warn of significant brand damage to Tesla from Musk's leadership role in the "Department of Government Efficiency," which has granted itself access to government databases with sensitive personal information and implemented thousands of job cuts.

Electric vehicle sales grew in several EU countries including Germany, as well as non-EU member Britain, the ACEA said, but they still only accounted for 15 percent of the auto market.

Musk in a conference call on Tuesday reiterated his bullish outlook on the long-term prospects for Tesla, highlighting its leadership in key growth areas: robotics, autonomous driving and artificial intelligence. (AFP)