"A lot has been written about how Agnetha and I fought and quarreled with each other. There is absolutely no truth in that," Lyngstad was quoted as saying by tabloid Aftonbladet. "Of course we competed, but to good effect."
The band has sold more than 370 million records and is famous for hits like "Waterloo," "Dancing Queen" and "Money, Money, Money."
After ABBA split in 1982, rumors of fights between Lyngstad and Faltskog swirled in articles and books about the band.
"No, we didn't fight. But we have to live (through) a whole lot of such misinterpretations," Faltskog said.
The two women came together Thursday to accept Aftonbladet's lifetime achievement award.
The four former ABBA members are rarely seen together in public, but were reunited in 2008 for the Swedish premiere of "Mamma Mia!" a film based on their hits.
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