In the public letter, the company reaffirmed that it was still interested in the business, which earlier in the month it made a bid of $10 billion for.
The letter also discloses more details about how it aimed to fund the acquisition, detailing the fact that it has already raised a total of $5 billion in equity from a number of sources.
The equity is being raised through Coty's parent company, Joh. A. Benckiser, a Germany-based family-owned business that also owns the Reckitt Benckiser personal care business.
Avon has steadfastly rejected the offer, claiming that it vastly under-values the real value of the business, calculated on the basis of its sales and profit margins.