Fragrance firm Coty has offered $10bn (£6.2bn) for beauty firm Avon Products.
Coty said it was not making a hostile bid, although Avon's management has refused to discuss the offer.
The bid represents a 20% premium on Avon's closing share price on Friday, but Avon said it "seriously undervalued" the firm and was "opportunistically timed".
Coty produces perfumes for celebrities including Lady Gaga, David and Victoria Beckham and Beyonce Knowles.
Avon is best known for its beauty products sold door-to-door, by women popularly known as Avon ladies.
Bart Becht, chairman of Coty, said: "Our objective is to engage in discussions with Avon and conduct due diligence, so that we and Avon can together determine if there is a basis for a transaction.
"We believe Avon's shareholders would want their board to explore with us the benefits to shareholders of a transaction."
Coty said it first approached Avon on 7 March with an offer of $22.25 per share. Avon management were not prepared to discuss that bid, so Coty raised its offer to the current level of $23.25 per share.
In a letter to the chief executive of Avon Products, Andrea Jung, Coty said: "We do not understand how your board's unwillingness to discuss our proposal can serve the best interests of Avon's shareholders.
"We believe, based on an extensive review of public information about Avon, that our proposed purchase price is a full and fair one."
Avon, which has been struggling with legal and business problems, said it was committed to finding a new chief executive.
"With a new CEO, Avon's board firmly believes that there is greater opportunity to improve shareholder value in excess of Coty's conditional indication of interest," the beauty firm said in a statement responding to Coty's offer.
Federal investigators are looking into allegations of bribery at Avon's operations in China. Regulators are also looking at whether the company had improper contact with financial analysts.
Avon reported a loss in its most recent quarter.