Championship leader Rosberg pipped his Mercedes team-mate by 0.013 seconds late in qualifying as he looks to cement a 23-point advantage over the Briton in the overall driver standings.
Hamilton has four races left after this weekend to overhaul Rosberg's lead but appears distracted off the track and announced he was planning a written media blackout in a post-qualifying news conference in the Mercedes area Saturday.
The 31-year-old refused to answer questions and said he was unhappy with media coverage of Thursday's news conference when he was criticised for playing with his phone -- adding bunny features to himself and rival racers on Snapchat.
"The smiles on your faces will probably be no longer," Hamilton told reporters Saturday. "I am not actually here to answer your questions, I have decided.
"With the utmost respect, there are many of you here that are super supportive of me. And those of you hopefully know I know who you are. There are others, unfortunately, that often take advantage of certain things.
"The other day [Thursday's press conference] was a super light-hearted thing, and if I was disrespectful to any of you guys, or if you felt that I was disrespectful, it was honestly not the intention. It was just a little bit of fun.
"But what was more disrespectful was what was then written worldwide... I don't really plan sitting here many more times for these kind of things so my apologies and I hope you guys enjoy the rest of your weekend."
Mercedes were unavailable for comment. Drivers are contractually obliged to speak to television crews after each session.
Hamilton, who won the title in 2008, 2014 and 2015, was set to regain the championship lead when he was leading with 15 laps remaining in Malaysia last Sunday but engine failure
forced him to retire and Rosberg took third to edge clear.
Hamilton did speak at the official media conference at Suzuka Saturday and claimed he was "happy" with qualifying.
"It has been a weekend of a lot of work trying to get the set-up right," he said. "Big changes before qualifying and considering that I am very happy with it. I did as well as I could.
"History has shown you don't have to be on pole to get the win but Nico has done a great job all weekend."
Rosberg, whose 0.013-second advantage equates to 82 centimeters around the 3.6-mile Suzuka circuit, told reporters he had felt comfortable all week.
"It was going well all weekend," Rosberg said. "Had a good balance, feeling comfortable and that's what allows me to put in a lap like that."