It will start the process immediately.
At its Monday price of 470.3p, the Government's stake is valued at Â£660m. There was no market reaction as the announcement came after the close of daily share trading.
Royal Mail's privatisation was heavily criticised after the shares almost doubled from their initial valuation.
The Department of Business, Innovation and Skills wrote: "Current market conditions should allow a successful sale and the realisation of value for the taxpayer.
"The universal postal service is strongly protected by law and Ofcom has a duty to ensure its provision. Therefore the government sees no policy reason to retain a stake in Royal Mail."
In June, the Government sold a similar-sized stake, which raised Â£750m.
As part of that sale, postal workers received a 1% stake in the company worth about Â£50m, in addition to the 10% given to them when the government started its sell-off in 2013.
It said in the summer that it intended to divest the rest of its holding before the end of the financial year.
The Government is selling the last 14% of its holding in Royal Mail to professional investors, two years after its initial privatisation.