Tensions between the 2014 F1 title rivals became open following qualifying in Monte Carlo, with Hamilton displeased when Rosberg secured pole position despite going off on his final Q3 lap, causing a yellow flag that prompted Hamilton to abandon his own pole bid.
Hamilton finished second to Rosberg in the race as well, and repeatedly expressed his frustration at Mercedes' strategy over the radio, particularly when he felt he should have been called in immediately when Adrian Sutil crashed in an incident that ultimately resulted in a safety car.
Asked if he felt the problems between him and Rosberg could now be solved, Hamilton replied: "I don't have an answer for you."
Rosberg was more conciliatory, insisting that there were no issues that could not be overcome.
"We've had discussions and we have known each other for so long, we always sit down and discuss it and move on, and that is what we will do," said the German, who now leads the world championship by four points.
He also declined to respond to comments Hamilton had made about his upbringing in an interview with the official F1 website earlier this week.
"I didn't hear Lewis say that so I am not going to comment, it is easy for you to just invent something," Rosberg said.
"Even if something like that was written, between what Lewis said and was written... I know Lewis would not say something like that, maybe to me, but not to the press."
Hamilton said a potential strategy change under the safety car was the only way he could have beaten Rosberg during the race.
"It is irrelevant now, but we got the exact same start and there are only two opportunities in the race, the pitstop is the other one," said the Briton.
"So the safety car came out at a perfect time for him and I didn't have a chance there.
"I think we have a rule that the guy in front gets the preference to pit first, I think that will be why."
Prior to Monaco, Hamilton had won four straight grands prix. Rosberg acknowledged that it was essential to halt that streak.
"It is a special win definitely because Lewis had the momentum, the results and everything and I needed to try to break that momentum and I managed to do that this weekend," he said.
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