"McLaren has the same engine as us and the car is sh*t," Mercedes' F1 chairman had told the Spanish newspaper El Pais.
"The same with Ferrari -- another sh*t car," the former Ferrari champion added.
After the publication of his blunt assessment, Lauda has now apologised privately and publicly to Ferrari.
"I apologise to Ferrari, to Luca Cordero di Montezemolo, and to the Italian fans. I should not have used that word," the great Austrian told Italy's La Gazzetta dello Sport.
"I was wrong and I do not make excuses. I called the president to explain my dismay," Lauda added.
"I have not seen the interview in the Spanish daily, but I was too heavy with my words -- forgive me."
Lauda also told the German newspaper Bild: "I explained to him (Montezemolo) and he understood. We have known each other for so long.
"I was asked a question about the difference between Mercedes and McLaren and Ferrari.
"I explained that Mercedes is simply the best combination of good car with the best engine, that McLaren also has the best engine but the car is not so good.
"And Ferrari has weaknesses on both sides," he added.
But Lauda made a point of saying Mercedes continues to regard Ferrari as a worthy opponent, particularly ahead of this weekend's Hungarian grand prix.
"I am even worried about the Ferraris in Budapest," he said, "because they have come much closer to us in the last races.
"Also Red Bull, who have a perfect car and only problems with the engine. But at the right moment also Ferrari can catch us on the wrong foot, as they are more dangerous than we thought before," Lauda insisted.
Also in the pages of La Gazzetta, Lauda made clear he actually does not regard Ferrari as having produced merely a "sh*t car".
"I have noticed at Hockenheim a Ferrari in progress," he said, "and I'm amused to see Fernando Alonso in the duels he has been in.
"I hope Kimi Raikkonen can recover, as he is a champion in a position that he does not belong."
As for Mercedes, Lauda sees the outcome of the 2014 championship as a straight fight between teammates Nico Rosberg and Lewis Hamilton.
"Lewis was unlucky at Hockenheim but drove a great race anyway, while Nico had obviously an easier time and won.
"The championship will be decided by the alternating fortunes and misfortunes of our two drivers. But the others are approaching and I understand that Ferrari will soon be very dangerous for everyone, starting with us," he added.
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