The players are protesting over reduced bonus payments for the finals in Gabon as well as payments owed from 2015.
"This has been happening for years and years. We always prepare well but there is always a problem with bonuses," said Norwich midfielder Youssouf Mulumbu.
DR Congo are scheduled to play Morocco on Monday in their first Group C match.
The Leopards reached the semi-final at the Nations Cup two years ago in Equatorial Guinea and finished in third place.
But the players insist they have yet to receive their financial rewards for the achievement.
DR Congo's sports minister Willy Bakonga has led a delegation of 100 officials to Gabon to resolve the problems.
He told Congolese radio: "When we arrive we will talk with them (the players). We will be together so there is no problem since the bonuses are already there. We'll give them to them.''
DR Congo's Everton winger Yannick Bolasie, who is missing the Nations Cup because of injury, told BBC Sport: "It is not a great situation because as a player you want to be focused on the first game.
"If three days before the first game you are concerned about not being paid and you are boycotting training, what kind of preparation is that?
"Even once you do get paid you can't just switch your focus and think everything is all right. You need three or four days to prepare - it is crucial.
"I understand the issues because I have been through it. When I have been with the squad I've tried to block it out because I don't want it to affect my game.
"This is the first time I am seeing the situation it from the outside the outside and it is really disturbing. The government should have sorted the issues so that everything is smooth.
"The player just want to be able to concentrate on the game but they haven't had the chance to do that."
The DR Congo squad boycotted their training session on Friday, just three days before their opening match at the Africa Cup of Nations.