"It's complete rubbish," the German, winner of nine grands prix so far this season, said as he and Hamilton joined factory-based employees on Tuesday to celebrate the team's third successive constructors' championship.
"He's on it as ever before, fully motivated and does massive work hours also. I've seldom seen that from him in the last years, such a large amount," he told Sky Sports television at the team's Brackley headquarters.
British media, whose criticism of Hamilton's use of Snapchat during a news conference in Suzuka led to a backlash from the driver who also walked out of another media session, had questioned his state of mind.
Monday's papers talked of a 'delicate ego', examined his 'fragile mental state' and suggested the Briton was losing it on and off the track.
"Executives were mouthing the word 'meltdown'," reported the Times newspaper, which said the champion had gone from "cocky prankster to sullen loser".
Mercedes motorsport head Toto Wolff said it was clear the media needed to produce headlines, building up and knocking down.
"Lewis had a couple of tough weekends... if he recovers and has a good weekend in Austin, he's the hero again," he said. "That's why I'm pretty relaxed about it."
The two drivers earlier visited the Mercedes high performance engines facility at Brixworth, where they also joined staff for a team photograph, signed autographs and posed for selfies.
Mercedes won the constructors' title in Japan at the weekend, a week after an engine failure denied Hamilton victory in Malaysia.
The three-times champion, who finished third in Suzuka on Sunday while Rosberg won, is now 33 points behind the German and even winning the last four races will not be enough if the other Mercedes finishes second.
No driver has ever won nine races in a season and not been crowned champion at the end of it, but Rosberg expected a tough battle right to the end.
"It's going to be an exciting end to the season for sure," the German told Reuters television. "A battle with Lewis as always, it's always tough against him.
"For me, it's just about looking at Austin. I'm excited to go there, I know I have the chance to win and I want to make it happen."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
