(Reuters) - Activist investment fund Starboard Value has taken a 4.5 percent stake in AOL Inc and is pushing for a meeting with the Internet company's chief executive and the board to address what it sees as strategic failings.

Starboard sent a letter to AOL CEO Tim Armstrong and the board on Wednesday in which it said AOL is deeply undervalued and blamed the company's massive operating losses in its display advertising business.

It also expressed concern over further acquisitions and investments in money-losing growth initiatives like its local service business Patch. Armstrong was an early investor in Patch before he joined AOL in 2009.

Armstrong has led the strategy to steer the company toward a display advertising and content business model similar to Yahoo Inc. Under Armstrong, AOL has spent nearly $700 million in acquisitions including high-profile names like Huffington Post and TechCrunch.

But even before he joined, AOL had made even bigger acquisitions to try to reinvent itself. It spent $850 million buying social networking site Bebo in 2008, which was sold for less than $10 million just two years later.

Starboard, which estimated that AOL may be losing more than $500 million per year in its display ad business alone, asked for an in-person meeting with the board to discuss how the company's operating performance and its valuation can be improved.

The fund, which manages assets in the upper hundreds of millions is looking to engage with the board ahead of its annual shareholder meeting on February 25, when directors will be up for re-election.

Shares in AOL have fallen some 40 percent since being spun off from Time Warner Inc in late 2009. Starboard argued in its eight-page letter that investors are now completely discounting the display advertising and content business that Armstrong has focused the business's future on.

Starboard said the market currently prices the entire business at around the value of AOL's declining dial-up Internet access business and its net cash position.

Armstrong has been trying to rapidly evolve AOL away from the shrinking but profitable business. The dial-up business is believed to be in long-term terminal decline as more Americans take up cable broadband and other faster connections.

While we understand and appreciate that the company's access business is in secular decline, we do not believe this serves as justification for continuing to pursue a money-losing growth strategy in the display business that has repeatedly failed to meet expectations, the letter said.

AOL argued in a statement that it has significantly reduced costs, sold non-core assets, made significant investments for our future, and also recently repurchased over 10% of outstanding shares, over the last two years.

The New York-based company also said it has a clear strategy and operational plan which will create shareholder value.

We will continue to aggressively execute on our strategy in 2012 as we continue the turnaround of AOL.

Miller Tabak analyst David Joyce, who has a buy rating on AOL, said he is broadly supportive of Armstrong's strategy to focus on media and advertising. He said after a difficult period AOL's display advertising business was starting to recover.

With the display ad growth coming through that's starting to help and their recent profits growth outpaced our estimates, said Joyce. There's momentum building in this strategy.

Starboard was spun off from Ramius LLC in March 2011 and is led by Chief Executive Jeff Smith. It describes itself as a value investor focused on U.S. small cap companies. Its investment team has previously been involved in shareholder activism with smaller medical and tech companies.

Shares in AOL were up 2 percent, or 29 cents, to $15.10 in afternoon trading on the New York Stock Exchange on Wednesday.