Appaloosa's billionaire founder David Tepper turned up the heat on the Botox maker one week after the company delivered disappointing earnings and shelved plans to sell its women's health business, which it had put on the block in May.

"In the wake of last Tuesday's earnings call ... it should by now be readily apparent to all interested and responsible parties that Allergan requires a fresh approach," Tepper wrote in a letter made public on Tuesday.

"We believed that the introduction of a seasoned independent Chairman with extensive pharmaceutical experience could exert a favorable influence on executive decision-making," the letter said.

Allergan's shares have fallen nearly 30 percent since October and are trading at less than half their historic high of more than $330 hit in 2015. On Tuesday, they were up 1.6 percent at $140.09.

The company undertook a review of its corporate strategy last year, but the result of that review may only be the sale of its relatively small infectious diseases unit and a commitment to remain disciplined in its spending.

Allergan said it had received the Appaloosa proposal and is "committed to continuing to engage with them." The company also said it is committed to strong governance practices and independent board leadership, and touted its pipeline of products in development.

Appaloosa, which oversees $12 billion, began pressuring Allergan to separate the roles, both currently held by Saunders, and to recruit an outsider to oversee its board in 2018. Tepper said that this is the fourth time he has written to the board to request this change.

Allergan's "moribund corporate performance and flagging stock price since our letters only deepens our conviction on this point," Tepper wrote. He also said splitting the roles is not a controversial move.

At the end of the third quarter, Appaloosa owned nearly 2 million Allergan shares, having cut its holdings by 41 percent, a regulatory filing shows.

Last year, both Appaloosa and Senator Investment Group wrote to Allergan urging the company's board to split the chairman and chief executive role and reconsider its acquisition strategy.

Analysts said that Allergan's disappointing earnings report last week made it vulnerable to more activist pressure.

(Reporting by Svea Herbst-Bayliss in Boston, Michael Erman in New York, Tamara Mathias and Manas Mishra in Bengaluru; Editing by Susan Thomas and Bill Berkrot)

By Svea Herbst-Bayliss