Cosmetics maker Avon changed course on a buyout offer it had previously rejected, declaring Sunday that it would consider selling itself to Coty after Coty sweetened the deal.

In a sparse two-sentence statement, Avon said its board would respond to Coty within a week.

Coty Inc. offered $23.25 for Avon on March 30, or about $10 billion. On Wednesday, Coty sent Avon a letter raising the price about 6.5 percent to $24.75 per share, or almost $10.7 billion. It demanded a response by Monday and said it would withdraw its offer otherwise.

Avon Products Inc., whose brands include Skin-So-Soft, Anew and mark, had told Coty that it wouldn't discuss any revised offer until its new CEO, Sherilyn McCoy, finishes reviewing all of Avon's operations, according to Coty's letter. Coty said it was disappointed; agreeing to sell itself would be Avon's best hope for a turnaround, the smaller company said.

Avon has been under pressure from a bribery scandal, possible credit rating downgrades, pinched profits and other problems. McCoy, a longtime Johnson & Johnson executive, became CEO just days after Coty made its offer.

Both of Coty's offers represent a premium to Avon's March 30 closing price of $19.36, the last trading day before Coty's offer was made public. Shares closed Friday at $20.19.

Privately held Coty is a beauty-products maker whose brands include Davidoff and Sally Hansen. Coty said its financing sources include Warren Buffett's Berkshire Hathaway Inc.

Founded in 1886, Avon became a fixture in households across the country as its legions of "Avon ladies" went door to door selling makeup to family members, friends and acquaintances.