Prime Minister David Cameron has described the outburst at police by Chief Whip Andrew Mitchell as "deeply regrettable" and said: "It must never happen again."
Mr Cameron was dogged by questions about the affair as he visited the United Nations in New York, despite trying over several days to draw a line under it.
He once again made clear that he did not believe matters should go any further.
Speaking at a brief press conference at UN headquarters, Mr Cameron said: "As I have said very clearly, he gave an apology, it was right he apologised, what happened was wrong, it shouldn't have happened and must never happen again.
"On the basis he has given an apology and the police have decided not to pursue that any further, that is where matters should rest."
Pressed in New York over why he appeared to accept Mr Mitchell's account of his tirade rather than that recorded in police logs, Mr Cameron said: "What I am saying very clearly is that what happened was wrong, it shouldn't have happened, it was deeply regrettable and that is why the Chief Whip has made a very public and clear apology.
"It was the right thing to do that. On the basis of that, on the basis of the fact also that the police aren't proposing to take matters further, that is how things stand."
Mr Cameron called Mr Mitchell in for a face-to-face meeting on Thursday, the day after his outburst, and told him his behaviour was unacceptable. In response, it is understood the Chief Whip looked the PM in the eye and said that he did not use the words attributed to him in reports but accepted he needed to apologise.
It emerged on Tuesday night that Mr Mitchell repeated his request to be allowed to cycle through the main gates the day after his outburst, but was again told to use the pedestrian entrance. But it is understood that there was no repeat of the angry confrontation on that occasion.
According to the 442-word police log - published in full in the Daily Telegraph - Mr Mitchell called officers "f****** plebs" and told them to "learn your f****** place".