Zoetis Inc. said its board has approved a $500 million share-buyback program, stepping up its efforts to avoid a potential takeover battle driven by activist investors.

The announcement comes a day after the animal-health products maker unveiled plans to buy Abbott Laboratories ’s animal-health business for $255 million and about a week after activist investor William Ackman disclosed a stake of about $2 billion in Zoetis.

In response to that move, Zoetis adopted a so-called poison pill plan, which is used to ward off potential takeovers, although the company didn’t mention Mr. Ackman’s Pershing Square Capital Management LP.

The company’s shares, which have risen 17% so far this month, were off about 1% in midday trading as the company hosted its investor day in New York.

At that meeting, the company projected slightly lower-than-expected results for next year. It guided for earnings, excluding items, of $1.61 to $1.68 a share on revenue of $4.85 billion to $4.95 billion, versus the respective estimates of $1.71 a share and $4.96 billion from analysts polled by Thomson Reuters.

Zoetis—a Pfizer Inc. spinoff that makes vaccines and medicine for household pets and livestock--generated $4.6 billion in sales last year, making it the biggest player in the animal-health industry.

The deal with Abbott would expand Zoetis’s diagnostics business as more people are having their pets treated for diseases such as diabetes and cancer.

The Wall Street Journal previously reported Mr. Ackman might push Zoetis to sell itself to a larger company, such as Valeant Pharmaceuticals International Inc. The report also said Mr. Ackman was working with Sachem Head Capital Management LP, another activist firm.

Write to Michael Calia at michael.calia@wsj.com