The move leaves Avon shareholders relying on new Chief Executive Sheri McCoy to come up with a plan to turn around a company that has been suffering from plummeting profits on falling sales at home and in some international markets, as well as a stock price that had been hammered prior to Coty's bid.

Coty last week raised its unsolicited bid, which had the financial backing of Warren Buffett's Berkshire Hathaway and others, to $24.75 per share from an earlier $23.25 per share offer, and gave Avon a Monday deadline to respond.

Avon, which had rejected outright all of Coty's earlier bids without entering into discussions, said on Sunday in a two-sentence statement that it would look at Coty's latest offer but respond within a week.

"Avon Products responded promptly to Coty's May 9 letter by disclosing it on May 10 and indicating that its board would consider the contents of the letter," Avon said in a statement early on Tuesday.

However, on May 14, five days after sending its letter, Coty withdrew its proposal, Avon said.

Coty, known for fragrances for celebrities like Madonna and Beyoncé, said that no one on Avon's board or senior management, including McCoy, returned its request for an explanation of why Avon needed more time to consider the bid.

"Your total lack of engagement with us leads us to believe that you remain reluctant to explore a friendly, negotiated combination on a reasonable timetable," Coty Chairman Bart Becht said in a letter to Avon dated Monday and made public. "Two months is enough."

Avon did not respond to a request from Reuters for comment.

Coty's reaction - take our offer by the deadline or we walk away - is consistent with how Buffett has approached dealmaking in the past. He has always been clear that Berkshire does not get into bidding wars; it makes what it considers a fair offer and that bid is either taken or not.

That was most recently seen last year with an offer by Berkshire's National Indemnity insurance unit for reinsurer Transatlantic. Amid a bidding war by other parties, Berkshire came in with a firm cash offer. It set a deadline, and when that deadline passed Berkshire simply withdrew its bid and went on its way.

A number of Avon shareholders had told Reuters in recent weeks that Coty's offers were too low but that they wanted Avon to at least meet with Coty.

Coty, which made its desire to buy Avon known to the public for the first time in April, had said from the start it had no intention of making a hostile bid for Avon, which has close to three times as much revenue as Coty.

Avon had rejected Coty's offers, arguing that they were too low and that the company's value could rise more from a turnaround led by a new CEO.

Avon shares had fallen 38.8 percent between the time they hit a 52-week high on May 16, 2011 and March 30, the last session before Coty went public with its overtures.

DECLINING SALES, FALLING PROFITS

Avon, is facing declining sales and a loss of sales representatives. Earlier this month, Avon reported weak first-quarter results, including a sharp drop in profits.

Avon has been bedeviled by heavy competition from drugstores in the United States, aggressive pricing by rivals in Eastern Europe and inadequate ordering systems that have frustrated representatives in Brazil, its biggest market.

The company has poured tens of millions into an internal probe into whether it broke the Foreign Corrupt Practices Act to build its business overseas. The U.S. government announced its own investigation last year.

Coty had said that before it could raise the offer any higher, it needed access to Avon's books to understand the financial implications of the U.S. probe as well as to get a sense of potential savings from combining the businesses.

When McCoy spoke to shareholders at Avon's annual meeting on May 3, she said her first priority was to stabilize the business.

McCoy, a former Johnson & Johnson executive, took the reins as CEO last month. She will conduct a thorough business review this year.

Fragrances accounted for 57 percent of Coty's $4.1 billion in sales in its year ended June 2011. The bulk of its sales come from Europe and North America. A tie-up would have given it access to developing markets such as Brazil, Russia and Mexico, and deepened its roster of products.

The companies first met to informally discuss a deal in February, initially exploring having Avon buy Coty. Becht last month said that when no offer came from Avon, Coty made a verbal offer, followed by three letters in March. Its original offer was for $22.25 per share.

Coty had lined up equity financing from several parties, including Coty's main shareholder, Joh. A. Benckiser, BDT Capital Partners and some of its limited partners, and Berkshire Hathaway. Coty had said J.P. Morgan Securities would provide debt financing.

Berkshire Hathaway would provide $2.5 billion of the financing, a person familiar with the matter told Reuters last week.

Shares of Avon closed up 77 cents on Monday at $20.96 on the New York Stock Exchange. Coty revealed its decision after U.S. markets closed.

(Reporting By Phil Wahba and Jonathan Stempel in New York. Additional reporting by Ben Berkowitz in Boston and Sakthi Prasad; Editing by Muralikumar Anantharaman and Mike Nesbit)

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