COPENHAGEN—Bain Capital and Advent International, together with Danish pension fund ATP, have agreed to buy Nordic card-payment company Nets for 17 billion Danish kroner ($3.14 billion) from a group of Scandinavian banks.

Nets handles payments in the five Nordic countries and has strong positions in Denmark and Norway. The company supports more than 33 million payment cards and over 500,000 merchants in the region, and handled more than six billion card transactions in 2013.

"We see a compelling investment opportunity to transform Nets from a strong Nordic company into a Northern European leader within the payments industry," said Carsten Stendevad, chief executive of ATP.

Robin Marshall, managing director and co-head of Bain's financial-services team in Europe, added in an interview that the consortium didn't have any plans to expand Nets outside of Northern Europe.

The buyers said they expect to eventually float Nets on a local exchange when it is ready but have no current plans to merge it with any other payment operations they own, such as Worldpay, which is jointly owned by Bain Capital and Advent International.