MILAN (Reuters) - Activist investor Elliott Advisors has built a stake in Telecom Italia (TIM) TLIT.MI (TIM), it said on Tuesday, in a move that could challenge the way top investor Vivendi VIV.PA runs Italy's biggest phone group.

FILE PHOTO: FILE PHOTO: Telecom Italia logo is seen at the headquarters in Milan, Italy, May 25, 2016. REUTERS/Stefano Rellandini/File Photo/File Photo

TIM shares rose as much as 7 percent, hitting their highest in more than four months, after news of the stake-building was first reported by Bloomberg. They closed up 5.95 percent.

Elliott may further increase its stake in the former state telephone monopoly and could take steps to replace some members of TIM’s board to improve governance, valuation, strategy and the company’s relationship with Italian authorities, the activist fund said in an emailed statement.

However, “it is not seeking to and will not seek control of Telecom Italia.”

TIM Chairman Arnaud de Puyfontaine, who is also Vivendi’s CEO, said the company “welcomed all investors”.

Founded by billionaire Paul Singer, Elliott is known for targeting companies where it believes the stock is undervalued and has waged campaigns at Anglo-Australian miner BHP Billiton BHP.AX and Dutch paints and coatings giant Akzo Nobel AKZO.AS.

Elliott owns both ordinary and savings shares at TIM, the spokesperson said without giving the exact size of the stake. The position in ordinary shares does not exceed thresholds triggering disclosure under Italian law, the person added.

For funds, the disclosure threshold in Italy is 5 percent.

TIM has lost more than one-third of its market value since French media group Vivendi first took a stake in mid-2015, unnerving other investors. Later on Tuesday, TIM is due to present a new strategy plan under recently appointed CEO Amos Genish, a favorite of Vivendi Chairman Vincent Bollore.

Investors hope the plan will set out a more aggressive course for the company, which has 26 billion euros ($32.24 billion) of debt. It is facing new competitors in both broadband and mobile and its only foreign business, in Brazil, is only gradually recovering from that country’s economic malaise.

The business plan “should increase further interest for this equity story. Finally, news flow on Elliott could add some speculative appeal,” Mediobanca Securities said in a note.

Genish is TIM’s third CEO in less than two years, leaving some investors guessing what is Vivendi’s ultimate aim for the company: use it as a pillar of its plan to create a southern European media empire or as an asset to trade in the next wave of mergers in European telecoms.

TIM has long been seen as a takeover target because it is smaller than many of its European rivals and it has first-mover advantage in Italy’s ultrafast broadband market.

Vivendi, which owns 24 percent of TIM, ousted Genish’s predecessor, who cut costs and boosted profitability but clashed with the top investor and Rome over a broadband rollout.

Vivendi has increasingly tightened its grip by appointing two-thirds of its board and naming its own chief executive as TIM’s executive chairman.

The hands-on approach led to tensions with Rome, which considers TIM of strategic national importance. Italy’s government eventually used the so-called “golden power” last year to ensure it had a say in some strategic decisions at TIM, a move widely seen as a bid to rein in Vivendi’s influence.

Genish undertook a charm offensive with the outgoing government and even proposed to separate the company’s network assets to boost transparency and smooth the relationship.

But the clashes between Rome and the phone group are bound to increase with the more radical government that is likely to emerge from last Sunday’s elections. The anti-establishment party that performed best in the vote has long called for TIM’s network assets to be state-controlled.

($1 = 0.8064 euros)