Ibrahim Toure, who had been suffering with cancer, died in Manchester on Thursday.
Reports had claimed the brothers would leave Brazil to be with their family as they mourn the passing of the 28-year-old, but a team spokesman said that they would remain with the national squad.
"The Toure brothers, Kolo and Yaya, have decided to stay with the team. They are not leaving Brazil," said a spokesman for the Ivorian Football Federation.
Ivory Coast face Greece in Fortaleza in Group C on Tuesday and a victory in that match will see them qualify for the last 16 of the competition.
Manchester City midfielder Yaya Toure played in the 2-1 defeat against Colombia, while Liverpool defender Kolo Toure was an unused substitute.