Activist investor Carl Icahn disclosed a 12.63 percent stake in medical device maker Hologic Inc, prompting the company to adopt a shareholder rights plan to protect itself from hostile takeovers.

Shares of Hologic, which makes screening tests for cancer and other diseases, rose 3 percent in late morning trading.

Icahn, who has a track record of taking big stakes in companies and pushing for management change, said in a filing with the U.S. Securities and Exchange Commission that he believed Hologic's shares were undervalued.

He also said he would consider discussing with Hologic's management the possibility of board representation and ways to improve shareholder value.

Icahn's move into Hologic is the first time that the billionaire investor has taken a stake of more than 5 percent in a healthcare company since his former top healthcare deputy, Alex Denner, resigned in late 2012, according to a Reuters review of Icahn's 13D filings.

Denner, who now runs activist hedge fund Sarissa Capital Management LP, was integral in a number of successful activist campaigns alongside Icahn, including pushing for the eventual sale of biotechnology companies Genzyme Corp, MedImmune LLC and ImClone Systems.

Hologic's shares have fallen 3 percent since November 11, when the company forecast lower-than-expected revenue for fiscal 2014.

A source familiar with Hologic, who declined to be named because he is not permitted to speak to the media, said any push to sell the company could result in its break-up.

"If Icahn pushes for a sale of the whole company, he might have a tough time," he said. "(I'm) not sure who would buy the whole thing. This could end up in breaking the company up."

Hologic's rights plan will be exercisable if a person or group acquires 10 percent or more of the company's common stock.

Hologic has been struggling with cuts in hospital spending and a lack of reimbursement for one of its mammography systems. In July, the company reinstated its former chief executive, Jack Cumming, in an attempt to turn around its fortunes.

Cumming, who was CEO of the company from 2001 until 2009, has been entrusted to undertake a full assessment of the company's businesses and to review the integration of Hologic's $3.75 billion acquisition of diagnostic test firm Gen-Probe Inc.

The deal, which gave Hologic access to Gen-Probe's diagnostics tests for blood diseases, transplant compatibility and sexually transmitted diseases, was widely believed to be an expensive deal for Hologic.

Hologic's shares have gained just 5 percent since April 30, 2012, when the Gen-Probe deal was announced.

In an interview on Monday with Reuters as part of its Global Investment Outlook, Icahn described his style of activism as relatively hands-off compared with that of some peers.

"We get involved on the board," Icahn said. "We don't micro-manage and, interestingly, we get invited back because we're not a disturbance or a disruption."

Hologic has a market capitalization of about $6 billion. Its shares trade at a multiple of 15.4 times its earnings, compared to a multiple of 21.4 times for healthcare equipment and supplies companies, according to Thomson Reuters data.

The stock was trading at $22.95 on the Nasdaq on Thursday.

(Reporting by Esha Dey in Bangalore and Jessica Toonkel in New York; Editing by Joyjeet Das and Saumyadeb Chakrabarty)