Lewis Hamilton called title rival Sebastian Vettel "a disgrace" after the Ferrari driver drove into his car in the Azerbaijan Grand Prix in Baku.
The two clashed before one of three restarts in a chaotic race, Vettel hitting the back of Hamilton's Mercedes and then swerving sideways into him.
Vettel said Hamilton had deliberately slowed - or "brake-tested" - him.
The Briton denied that and said Vettel's driving was "disgusting" and "not sportsman's conduct".
Vettel of Germany was given a 10-second stop-and-go penalty in the race - won by Red Bull's Daniel Ricciardo - after being found guilty of dangerous driving but still finished a place ahead of Hamilton in fourth, extending his championship lead to 14 points.
The 29-year-old was also given three penalty points on his licence, taking him up to nine. If a driver receives 12 in a 12-month period, it triggers an automatic race ban.
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If Vettel receives three penalty points at the next race in Austria on 9 July, he would face a race ban. However, two points will drop off after the British Grand Prix on 16 July as he was punished for forcing Felipe Massa off the track at Silverstone last year.
Hamilton was not penalised. The stewards examined data from his car and found that he had maintained a more or less constant speed, had not lifted off the throttle or braked, and had behaved no differently at that restart at that point on the track than at the other two restarts.
Hamilton appeared not to accelerate out of Turn 15, the penultimate corner, and Vettel hit him up the back, damaging the Ferrari's front wing and part of the Mercedes' floor.
Vettel then pulled alongside Hamilton and swerved into him, banging wheels.
Asked if he drove into Hamilton deliberately, Vettel said: "It was very clear. We are racing with men. I don't have a radio to him. If we get a penalty, we should both get a penalty."
He added: "I wasn't happy with the brake-testing. I drove alongside him and raised my hand to say that is not the way to do it and we had a little contact."
Vettel added that it was "quite obvious" Hamilton had brake-tested him.
"I don't run into the back of him on purpose," he said. "I damaged my wing; he had a little damage as well.
"His restart was really good; I didn't think it was necessary. The problem is me right behind getting ready and all the other cars.
"He did something similar a couple of years ago in China at the restart. It is not the way to do it.
"The leader dictates the pace, but we were exiting the corner, he was accelerating and then he braked so much that I was braking as soon as I saw and I could not stop in time and ran into the back of him. That was just not necessary."
Vettel was unaware immediately after the race that his penalty was for swerving into Hamilton. He said that he thought the penalty must have been for hitting Hamilton from behind.
Hamilton, who lost victory in the race because he had to pit to have a loose head restraint fixed, responded: "I didn't [brake-test him]. I controlled the pace. All the restarts I slowed down in the same spot.
"He was obviously sleeping and driving alongside and deliberately driving into a driver and coming away scot-free is a disgrace. He disgraced himself.
"If he wants to prove he's a man, we should do it out of the car face-to-face. Driving dangerously in any way can put another driver at risk.
"Luckily we were going slow. If we were going fast it could have been a lot worse. Imagine all the kids watching Formula 1 today and seeing that kind of behaviour from a four-time world champion. It says it all."
Asked if things had got dirty in the title fight, Hamilton said: "Not for me. I am going to keep going.
"We had the upper hand this weekend. We can continue to move forwards in the future. Through difficult times true colours show, so it is a good day for me."
Vettel said the fight was "still respectful", adding: "I don't have a problem with him. It is just one action today that was wrong.
"I am willing to sort it out with him. I don't think there is much to sort out. I will talk to him when you (the media) are not there and then we move on."
Asked if he expected Vettel to apologise, Hamilton said: "I don't fancy seeing him. It might turn into something else."
Mansell's reaction - and #bbcf1
Frazer Shaw: Whether Hamilton brake-checked Vettel or not does not excuse using your vehicle as a weapon for the second hit. Outrageous behaviour.
Alex Rose: So Vettel drives into Hamilton, gets a penalty and still manages to finish in front. That's not right.
James Sunman: What Vettel did to Hamilton would be a black flag even on a karting stag do, never mind the biggest racing series in the world.
Alex Withington: The repercussions will go on for a while after this one. Both Vettel and Hamilton will feel they were wronged. F1 2017 looking tasty.
Steven Coy: The Vettel/Hamilton doesn't need penalties, the fierce competitiveness between these two is what this sport needs!
Andrew Ogley: Well, frankly that was all a bit bonkers today.