Its offer for Mylan, of $82 a share split between cash and stock, represents a 38 percent premium to Mylan’s stock price before it offered to acquire Perrigo. Shares of Mylan rose nearly 9 percent in New York, to $74.07.

Another factor inspiring big companies to make big deals is the continuation of low interest rates, so debt is incredibly cheap, said Ken Cacciatore, an analyst at Cowen & Company.

“They realize — like any management team should in any industry — that in this interest rate environment they should create value using any means possible,” Mr. Cacciatore said in an email.

Mylan declined to comment on either the Teva offer or the Perrigo rejection.

But last week, Mylan took the unusual step of announcing it was uninterested in a takeover from Teva, even before such an offer had been made.

“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’s executive chairman, Robert J. Coury, said in a statement. “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.”

That was only the latest indication of Mylan’s desire to remain independent. Its offer for Perrigo was viewed as a defensive move because Teva was known to be interested in a takeover of Mylan at the time.