The Spain coach Del Bosque fears for the impact on the national team after spiky exchanges between the clubs during Champions League semi-finals.
Barca-Real rivalry threatens to 'divide' world champions Spain
The two clubs — who supplied the bulk of Spain's line-up at the tournament in South Africa last year — were involved in a series of spiky exchanges before their series of four matches in the space of 18 days in April and May.
Jose Mourinho, the Real coach, was handed a five-game ban by Uefa after he made allegations of favouritism towards Barcelona following Real's 2-0 defeat in the first leg of their Champions League semi-final tie.
"We will have to heal the wounds as soon as possible. The clashes have left their mark because there are people who use the Madrid-Barcelona rivalry to divide and disengage," Del Bosque told a Barcelona-based newspaper La Vanguardia.
"We will look for solutions, without abusing diplomacy. I hope all this mess with so many matches does not contaminate us too much because it would be a serious mistake.
"During a competition there sometimes is friction but you should never lose respect. If we want to be champions, if we want to continue on the path to success, we need to maintain a good atmosphere."
Del Bosque, who has led the national team since 2008, led Real to two Champions League titles and a pair of league championships before he was unceremoniously dismissed as coach in 2003.
Asked if he would ever return to Real, the 60 year old said: "No, never. Nothing would make me change my decision. I will not return to Madrid but I have to say that, as an institution, the club gave me everything and I don't feel they have a debt towards me."
Mourinho's appeal against the five-game ban will be heard on July 29. Barcelona went on to win the Champions League, beating Manchester United 3-1 at London's Wembley Stadium last month. They also won the Spanish Primera Liga.
"Barcelona really is at the moment one step above the rest," said Del Bosque.
"But I see teams out there that are also very strong and the moment will come when they can also lose. Barca have shown that they are better, but in football no one is invincible."
* Agence France-Presse
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