The writedown - discussed for five hours during a seven-hour board meeting - surprised investors, including Vivendi, which has a 24 percent stake. A spokesman for Vivendi said its representatives on the Telecom Italia (TIM) board voted against the decision.
"We found it shocking," the spokesman said, adding he saw the decision as "very unusual and very destabilising".
TIM shares closed down 4.8 percent on Friday.
The former telecom monopoly has been caught in the middle of a struggle between Vivendi and activist fund Elliott, which eventually wrestled board control from the French group at a shareholder meeting in May.
The position of CEO Amos Genish, appointed by Vivendi, has come under pressure from tougher competition at home and the increasingly bitter war of words between the two main investors.
In a recent interview with La Repubblica daily Genish said the situation within TIM was "becoming unsustainable" and that "greater alignment between shareholders, management and the board were needed" to support the company's growth.
"I hope and expect all board members and shareholders will be supportive of progress in governance," he told analysts on Friday in a call on nine-month results.
Under Genish TIM is working on a three-year turnaround plan focussing on a digital transformation and fixing finances.
Since May, Vivendi has blamed Elliott for TIM's falling share price. On Friday, Vivendi pointed to a "total lack of governance" and "total disorganisation" at TIM.
Asked whether Vivendi would call a shareholder meeting to push for a board reshuffle, the spokesman said: "Vivendi will not rule out anything to protect its interests."
Elliott had no immediate comment. The fund has in the past urged Vivendi to work on constructive solutions at board level.
The 2 billion euro writedown overshadowed the operational results at TIM, Italy's biggest phone group, which analysts said were reassuring despite tough competitive conditions.
"The mobile business is proving to be much more resilient than we expected," Bernstein analysts said in a note.
Broadband group Open Fiber is rolling out a rival fibre optic network to TIM's, while French telecoms group Iliad has launched a low-price mobile offer for Italy.
The incumbent's finances have also been stretched after it bid 2.4 billion euros - much more than initially planned - to secure airwaves in Italy's fifth-generation mobile auction.
"The worst impact (from Iliad entry) is over," Genish said.
The CEO, who until end 2016 was CEO of Telefonica Brasil, said the group was interested in NII Holdings' Nextel unit in Brazil. Sources said TIM's board had given its OK for a non-binding offer for Nextel.
"We are in an initial non-binding phase," Genish said.
He said TIM was "very long" on Brazil, adding while growth would be mainly organic, M&A in spectra could be on the cards.
"Fixed infrastructure could also be of interest but there is no major target yet," he said.
TIM said comparable earnings before interest, tax, depreciation and amortisation (EBITDA) in the first nine months fell 2.9 percent to 6.03 billion euros), roughly in line with an analyst consensus provided by the company.
Including the writedown, the company reported a net loss of 800 million euros.
Sales in the period fell 3.1 percent to 14.22 billion euros, in line with expectations, while adjusted net financial debt stood at 25.19 billion euros at the end of September.
TIM also abandoned its 2018 net debt to core earnings target of around 2.7 times, because of a fine imposed earlier this year, an adverse competitive and regulatory environment at home and a weaker exchange rate in Brazil, its only foreign market.
The company should reach the 3 times target it achieved last year, its CFO added during the analyst call.
(Editing by Jane Merriman and David Evans)
By Agnieszka Flak and Stephen Jewkes