LONDON/MILAN (Reuters) -Nvidia ( NVDA ) stock rose in Europe on Wednesday, suggesting shares in the company at the heart of the artificial intelligence markets boom may recover further after a steep drop this week triggered by the rise of China's DeepSeek AI tool.

European technology stocks also got a lift, fuelled in part by an 11% surge in shares of ASML after the Dutch-listed company, which makes tools to manufacture computing chips, including those used in AI applications, reported a surprisingly large rise in new bookings.

Nvidia's ( NVDA ) Frankfurt-listed shares rose 2%, having closed up 8.9% on Wall Street on Tuesday.

The emergence of DeepSeek's suite of AI tools as possible challengers, not just to incumbents such as OpenAI's ChatGPT, but as a sign development costs may be dropping rapidly, battered AI-linked stocks on Monday, wiping billions in market value off Nvidia ( NVDA ), as well as other technology companies.

Shares in Nvidia ( NVDA ), whose chips are commonly used in AI, fell 17% on Monday, which cost the company almost $600 billion in market value - the largest single-day drop in market capitalisation for any company on record.

Nasdaq futures were up 0.4% in morning trade in Europe, suggesting the cash index could extend Tuesday's 2% rise. An index of European tech stocks, which on Tuesday fell 3.5%, was up 4.5%, heading for its biggest one-day jump in a year.

Much of that rise was powered by ASML, but shares in chipmakers BE Semiconductor and ASM International were also up 6-7%.

"Nvidia ( NVDA ) is not a lone wolf. At the end of the day, Nvidia ( NVDA ) carries with it more than $10 trillion of market cap of affiliated companies, whether they're doing nuclear, industrial equipment, suppliers to Nvidia ( NVDA ). So it's a galaxy, not just the one company," Jacques-Aurélien Marcireau, co-head of equities at Edmond de Rothschild Asset Management, said.

DeepSeek launched a free AI assistant last week that quickly overtook OpenAI's ChatGPT on Apple's App Store in the United States and the cost and performance of the company's AI tools seemed to upend the belief in the industry that China was years behind its U.S. rivals in the AI race.

By Wednesday, there was a greater sense of calm across markets, as investors focused on upcoming earnings from several of the so-called Magnificent Seven U.S. megacaps, which count Nvidia ( NVDA ), Apple and Microsoft among their ranks.

"While questions remain unanswered, the market is voting that the innovation that DeepSeek could bring to the ecosystem will unlikely impact the AI capex cycle and could even lead to new channel of demand for GPUs (graphics processing units)," Pepperstone strategist Chris Weston said.

Separately, Microsoft and OpenAI - run by Sam Altman - are probing if data output from the ChatGPT maker's technology was improperly used by a group linked to DeepSeek, Bloomberg News reported on Tuesday.

(Additional reporting by Danilo Masoni in Milan; Editing by Bernadette Baum and Louise Heavens)