This week, members of the union have begun another round of strike action in locations including Coventry, Nottingham, London and Northern Ireland.
Mandelson has rebuffed various calls to step in and intervene, despite union leader Billy Hayes accusing ministers of "sulking", according to the BBC.
Hayes said: "There hasn't been one government minister, at any level, talking about the strikes, which have disrupted services."
He added that some government ministers "are sulking" because of the ongoing battle to part-privatise Royal Mail.
However, according to the BBC, Mandelson said strike intervention with the CWU would not happen.
"It is time for the union to wake up to the need for change to stop the Royal Mail's further decline," he added.
Recent strikes have involved more than 12,000 Royal Mail employees walking out with companies being warned that ongoing action could lead to clients turning away from direct mail.
Lord Mandelson tells CWU to 'wake up' over strike action
Business Secretary Lord Mandelson has told the Communication Workers Union (CWU) to "wake up" in order to stave off a further decline in the services of Royal Mail.
