Around 42,000 mail centre staff and network drivers will stage a 24-hour walkout on Thursday 22 October, swiftly followed by 78,000 delivery and collection staff following suit on 23 October.
Dave Ward, deputy general secretary at CWU, said: "We made a genuine offer to Royal Mail that would have given space for detailed discussions without a strike."
He said: "We were severely disappointed that, within two or three hours, the company rejected it, apparently without even affording it proper consideration.
"This comes on the back of several rejections of CWU offers and is a clear indication that they are not trying to reach agreement."
In the letter, Ward outlined an eight-point offer to help "restore customer confidence" in the mail operator at a time when companies such as Amazon and House of Fraser are dropping lucrative contracts with Royal Mail.
Earlier in the week, business secretary Lord Mandelson condemned strike action by Royal Mail CWU members as a "suicidal act" that "defies logic" and one that could turn customers away from the mail medium.
The CWU also called on the government to intervene, claiming such action would help source an agreement to the problem.
"This government has recently intervened in the problems of Vauxhall and Lloyds Bank. They are the sole shareholder of Royal Mail and it is unbelievable that they continue to stand aside," he added.
Royal Mail previously called the possible of strike action "totally unjustified".