(Reuters) - Teva Pharmaceutical Industries Ltd on Tuesday made an unsolicited $40 billion offer for smaller rival Mylan NV, a bold bid for growth as its lucrative Copaxone drug faces generic competition.

The offer followed weeks of speculation that Israel-based Teva, the world's largest generic drugmaker, would soon target Mylan. Shares of Mylan traded below the offer price of $82 in cash and stock, evidence of investor skepticism that Teva can win over the company, which has set up a defense that includes a poison pill.

Analysts agreed that Teva would need to sweeten its bid to the $90-per-share range. S&P Capital IQ analyst Jeffrey Loo said a viable offer would be $92, about 22 times Mylan's 2015 expected earnings.

"If they raise their bid, they will have more Mylan shareholders pressuring management to come to the table," Loo said. He suggested Teva would need to increase the cash component of the offer, which is now at 50 percent.

Perrigo has not yet responded to that offer, saying it would consult its board, but a source familiar with the matter said the company was set to reject Mylan's bid as soon as this week.

Mylan Executive Chairman Robert Coury said last week that the company had studied the potential for a deal with Teva and concluded that such a combination "is without sound industrial logic or cultural fit," and would attract antitrust scrutiny.

Teva said its offer should be more attractive to Mylan shareholders than the proposed purchase of Perrigo, representing a 48 percent premium to the company's share price before speculation of a deal surfaced on March 10.

Pressure has been growing on Teva for new revenue sources as multiple sclerosis drug Copaxone starts to face generic competition this year.

Teva said the purchase would help it to expand its offering of harder-to-produce medical products, such as soft-gel caps, topical and inhalant technologies and injectables, and increase its portfolio of specialty pharmaceuticals.

The acquisition would create an entity with more than $30 billion in annual revenue, add to earnings in the first year and eventually generate $2 billion in annual savings, Teva said. It expects that a transaction could close by the end of 2015 and pledged a quick response, including selling assets if necessary, to ease any regulatory concerns.

Mylan shares were up 8.9 percent at $74.12 in afternoon Nasdaq trading, while Teva rose 2.0 percent to $64.55 on the New York Stock Exchange. Perrigo fell 2.2 percent to $193.79.

HEALTHCARE DEAL FRENZY

A Teva-Mylan deal would be the second-largest healthcare transaction in the last 12 months, following generic drugmaker Actavis Plc's $66 billion purchase of Botox maker Allergan. The wave of consolidation has also included AbbVie Inc's proposed purchase of Pharmacyclics and Valeant Pharmaceuticals' deal for Salix.

Generic drugmakers are looking to get bigger and gain access to product lines with higher profit margins, while traditional pharmaceutical companies have tried to add novel treatments for cancer and rare diseases.

Teva Chief Executive Officer Erez Vigodman said the companies should meet to address Mylan's concerns. In a letter to Coury, he said a deal would create "an organization with the scale and reach to excel in the current environment, which I know you appreciate."

A turnaround specialist, Vigodman joined Teva last year, tasked with cutting costs and improving profits under pressure from rising competition. In February, he said the company was ready to return to making acquisitions. A Mylan purchase would be the largest deal in Israeli history.

Mylan recently moved its headquarters from the United States to the Netherlands, where corporate taxes are lower and where it could take advantage of Dutch anti-takeover provisions that can dilute shares by granting a call option to a foundation set up for this purpose.

In early April, Mylan said it had entered into such a call option agreement.

Sanford Bernstein analyst Aaron Gal said in a research note that Perrigo was likely to reject Mylan but might then start negotiating with the company. That would push Mylan to campaign to win shareholder support for its purchase.

At the same time, Teva will start its own campaign to publicly convince Mylan shareholders of the merits of its offer. Mylan is likely to demand a higher price, shared management and maybe some employee job protection, he said.

Barclays and Greenhill & Co Inc are advising Teva, whose lawyers are Kirkland & Ellis LLP, Tulchinsky Stern Marciano Cohen Levitski & Co, De Brauw Blackstone Westbroek N.V. and Loyens & Loeff N.V.