The 26-year-old insists the players have put aside their rivalry following a flare-up between the sets of players during a previous friendly match with Chile
A scuffle ensued on the pitch in a friendly encounter with Chile in 2011, with players from both clubs becoming embroiled in confrontation with each other as well as with the opposition.
Speaking ahead of the meeting of the sides on Tuesday, Fabregas feels there is now far greater unity within the Spain squad and believes further success is dependent on such a positive atmosphere.
"I remember what happened in that friendly in Switzerland two years ago," he told reporters.
"There was a lot of tension between the players of Real Madrid and Barcelona at the time, but we came together.
"Now there is a great atmosphere. We are very professional and know how to separate the difference in our clubs.
"We fight for the same goal, which is one of the keys that has brought us good results."
Fabregas also expressed his delight at being a regular in Vicente del Bosque’s starting XI and called on his side not to underestimate Tuesday's opponents, especially having been warned by Barca team-mate Alexis Sanchez of Chile's desire to avenge their World Cup defeat.
"Every time I am selected I feel more important. It makes me feel special and want to play on," the 26-year-old continued.
"Chile are warriors and tend to run around a lot if you let them. They are very competitive are very talented, with important players playing in big clubs. I'll have to go out and compete.
"I talked to Alexis about the match. He tells me they are very motivated and are eager to beat us in revenge for what happened in the last friendly and in the World Cup."