Beauty company Coty Inc said on Monday that it had offered to buy Avon Products Inc for $10 billion and was willing to raise the price, but the bid was rejected by the cosmetics direct seller, which faces sliding sales in key markets and a bribery probe.

Coty, whose products include fragrances by celebrities including Beyonce and Lady Gaga, said it had no plans to make a hostile bid, but had been "unsuccessful" in getting Avon to talk about a deal.

The fast-growing privately held company majority-owned by Joh. A Benckiser, is offering $23.25 per share, a 20 percent premium over Avon's Friday closing price of $19.36 on the New York Stock Exchange.

Shares of Avon rose 17.8 percent to $22.80 in morning trading.

In a statement on Monday, Avon rejected the offer, saying it "substantially undervalues" the company.

But analysts said Avon's board should not dismiss the bid out of hand, given the company's problems.

"It's an opportunity that the board should seriously consider," said Sanford C. Bernstein & Co analyst Ali Dibadj. Except for perhaps another direct seller, he added, there are few potential suitors for Avon.

Coty's bid is not "dramatically too low," he said, predicting Coty will come back with a higher offer.

Avon is searching for a new chief executive officer to replace Andrea Jung, who has held that post since 1999. It has said the new CEO will undertake a top-to-bottom review of the struggling company, which is dealing with a probe into whether it broke U.S. anti-bribery laws in China.

Avon, which is also cutting jobs, said that having a new CEO will create a "greater opportunity" to increase its value beyond what Coty is offering.

The company is facing a long decline in sales and the number of sales representatives in the United States. During the holiday period, sales fell in key emerging markets like Brazil and Russia.

For Coty, buying Avon would allow it to depend less on fragrances and perfumes and branch out more into cosmetics and skin care products. The company praised Avon's presence in emerging markets, an area where it wants to grow.

Coty got 57 percent of its $4.1 billion in sales in fiscal 2011 from perfumes, and revenue is still heavily skewed toward the United States and Europe. Overall revenue was up 17 percent in the last fiscal year.

In recent years, Coty has done deals aimed at becoming a more diversified beauty company. In 2010, it acquired Philosophy Inc, a maker of personal care products, from Carlyle Group for $1 billion and bought a majority stake in Chinese skin-care company TJoy Holdings Ltd.

Coty also said Avon's door-to-door direct sales model would help its beauty brands.

It said it would call the new company "Avon-Coty."

Coty said it originally offered Avon $22.25 per share in early March, but failed to entice the company into talks. It said it went public with its latest offer after sending three letters to Jung, but failing to draw Avon into discussions.

"We do not understand how your Board's unwillingness to discuss our proposal can serve the best interests of Avon's shareholders," Coty Chairman Bart Becht said in letter to be delivered to Jung on Monday.

Coty said it would be willing to raise its offer if Avon can show there is greater value in the company by opening its books. Coty said it was confident it can line up the necessary financing to pull off the acquisition of a company with sales three times greater than its own.

At Friday's close, shares of Avon were down nearly 50 percent from a year and a half ago. Before Coty made its bid public, Avon was worth only about $8 billion, down from an all-time peak of $21.8 billion in June 2004.

(Reporting by Phil Wahba in New York; Editing by Lisa Von Ahn and John Wallace)