Teva Pharmaceutical Industries Ltd. has made a proposal to acquire drug maker Mylan NV for $82 a share in cash and stock, a sign of the jockeying for dominance among generic drug makers.

Earlier this month, Mylan made an unsolicited $28.9 billion proposal to buy Ireland-based Perrigo Co. Teva's bid represents an effort to disrupt that.

Shares of Mylan, up 25% over the past three months, closed Monday at $68.05.

Mylan, following The Wall Street Journal's report last week of Teva's possible offer, said then that it is committed to the Perrigo deal.

"We have studied the potential combination of Mylan and Teva for some time, and we believe it is clear that such a combination is without sound industrial logic or cultural fit," Mylan said Friday. "Further, there would be significant overlap in the companies" businesses, and we believe that it is unlikely that any such combination could obtain antitrust regulatory clearances."

Teva has largely remained on the sidelines of a frenzied deal market in the health-care space, but it has indicated in recent months it has an appetite for entering the fray.

A tie-up would create a generic drug giant, which could use the combination to cut costs and cope with rising competition. Ruminating about a Teva-Mylan combination, J.P. Morgan has estimated such a deal could lead to more than $1 billion in annual cost savings.

Write to Tess Stynes at tess.stynes@wsj.com

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