The Finnish paper producer said last August that it was considering reducing its 50% stakeholding in the merchant.
The dilution of interests was announced by the then incoming president and chief executive Hannu Anttila, along with a 304m rights issue.
In the UK the Map Merchant Group comprises James McNaughton, Premier Paper and gm2 logistics.
Corporate communication vice-president Jyrki Antikainen said the company had taken the decision as the merchant was an important sales channel.
Map Merchant Group has sales of 1.3m tonnes per annum across Europe, almost half of which comes from M-real.
M-real has also stopped talks on the sale of its folding carton plants.
The firm had been in talks with several parties, but Antikainen said: "there were no good deals around."
M-real has five folding carton plants, two in Finland, two in Belgium and one in Hungary.
Story by Andy Scott