Avon Products Inc. (AVP) said the U.S. Securities and Exchange Commission proposed last month a potential settlement to resolve a multiyear bribery probe with monetary penalties "significantly greater" than the beauty-products company previously suggested, and it warned such a settlement would materially hurt its business.

The bribery probe has dogged Avon since 2008, costing it hundreds of millions of dollars in legal and other bills relating to an internal investigation, according to securities filings. The investigation centers on whether Avon violated the Foreign Corrupt Practices Act by making payments or providing gifts to officials in China to secure licenses to sell its products there. It began with a tip to former Chief Executive Andrea Jung and spread to other countries, including key markets in Latin America.

"We disagree with the SEC staff's assumptions and the methodology used in its calculations and believe that monetary penalties at the level proposed by the SEC staff are not warranted," Avon said Thursday in a filing with the SEC, without disclosing the size of the proposed settlement. If the company were to enter into settlements with the SEC and Department of Justice at such levels, Avon said its earnings, cash flows, liquidity, financial condition and ongoing business "would be materially adversely impacted."

The company said in August it has offered $12 million to settle the probe, a deal that was rejected. The Wall Street Journal has reported Justice Department and SEC officials expressed their belief in early discussions that Avon's penalty should exceed $100 million, citing a person familiar with the matter.

The company also reported swinging to a third-quarter loss as the door-to-door cosmetics vendor recorded a drop in sales amid headwinds in North America and China.

Shares fell 5% to $21.27 in light premarket trading as both the top- and bottom-line missed Wall Street's expectations.

"The third quarter was tough," said Chief Executive Sheri McCoy. "Our quarterly performance was negatively impacted by macroeconomic headwinds and continued weakness in some parts of our business, particularly North America," which saw sales fall about 19%.

The China operations, meanwhile, posted a 67% decline in revenue, due in part to a decline in unit sales. Avon said the company recorded a write-down of $42 million and a valuation allowance for deferred tax assets related to China that hurt per-share earnings by 12 cents in the period.

The New York-based company is trying to reverse a years-long slide in sales and has also been facing questions about its business model, which depends largely on sales generated by women who sell makeup, perfumes and lotions to friends and family members.

Under Ms. McCoy, who was hired in April 2012 to replace long-running Ms. Jung, Avon has been cutting costs and jobs and exiting some markets where it underperformed, including South Korea, Vietnam and Ireland. The U.S. and U.K. have also been weak spots for Avon, but Ms. McCoy said she is committed to turning around the business in those countries.

Overall, Avon reported a quarterly loss of $5.5 million, or a penny a share, compared with a year-earlier profit of $31.6 million, or seven cents a share. Excluding the impairment charge related to the company's China operations, restructuring charges, the negative impact of the devaluation of Venezuelan currency and other items, adjusted earnings from continuing operations totaled 14 cents a share.

Total revenue fell 7.5% to $2.32 billion, or 1% in constant dollars.

Analysts polled by Thomson Reuters recently projected earnings of 19 cents a share on $2.44 billion in sales.

Sales in the main beauty business fell 6% to $1.66 billion. Sales in Latin America--which accounts for the bulk of the company's business--were down about 5% at $1.21 billion.

Through Wednesday's close, the stock has risen 56% since the start of the year.

Write to Anna Prior at anna.prior@wsj.com

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