Botox-maker Allergan should split its chairman and CEO roles, bring in new leaders and remake its board, according to a letter from Appaloosa Management's David Tepper on Tuesday.

Tepper, whose hedge fund owns just 1 percent of the drugmaker's shares, is pushing for a management overhaul days after CEO Brent Saunders outlined a plan to sell Allergan's women's health and infectious disease businesses. The plan resulted from a strategic review that also looked at splitting up the company or doing acquisitions.

"It is time for Allergan's management to concentrate on running a world class pharmaceutical and aesthetics business and forego thoughts of, or the exhilaration from, an ambitious acquisition strategy," Tepper wrote in a letter to Allergan's board. The letter was also signed by Douglas Silverman of Senator Investment Group.

"We were underwhelmed by the Company's half-hearted attempt to restore strategic momentum," the letter said.

Allergan shares rose 0.7 percent Tuesday but are down more than 6 percent year to date.

In a statement, Allergan said its board and management "welcome" input from shareholders and take their views into account, but it didn't address Tepper's demands for management change. Instead, it said its recently concluded strategic review was designed to create a "more focused" Allergan. It has added three new directors since the beginning of last year and prioritizes "board refreshment."

"Our number one priority continues to be executing on operational excellence and delivering strong results to drive long term shareholder value," the statement said.