“It calls for two fundamentally different and conflicting cultures to be integrated under a board and leadership team with absolutely no proven ability to deliver sustainable shareholder value,” Mr. Coury wrote.

Mr. Coury also highlighted the possibility that a merger of Mylan and Teva would be blocked by antitrust regulators, pointing to Comcast’s recently ended bid for Time Warner Cable. Any potential deal would need to include provisions for undertaking any and all actions necessary to win government approval in a short period.

At times, Mylan’s rebuff of its competitor appeared to verge on the personal. Mr. Coury criticized Teva’s unsolicited takeover bid as unnecessarily bare-knuckled and coming out of the blue.

“Through your leadership, you had the opportunity to set the right tone, and show the world that there is a new Teva,” Mr. Coury wrote in the letter, which was addressed to the Teva chief executive, Erez Vigodman. “Instead, you chose to approach Mylan in a way that demonstrates that the old Teva is very much still alive, which only continues to beg questions about Teva’s credibility.”

In a statement, Teva said that it was committed to pursuing a takeover of its rival, one that it pledged to complete as soon as possible. The Israeli company reiterated that its offer represented a 38 percent premium to the trading price for Mylan shares before it offered to buy Perrigo.

“While we are disappointed that Mylan has formally rejected our proposal, the Teva board and management team are fully committed to completing the combination of Teva and Mylan, and we stand ready to quickly complete a transaction that is compelling for both Teva and Mylan stockholders,” Mr. Vigodman of Teva said in a statement.