Mr Elliot accused him of going back on his word and said, "Occupy Wellington does not deal with grandstanding.''
The crowd cried out that they wanted Mr Peters to speak, and Mr Elliot gave him the microphone.
But Mr Elliot switched the loudspeaker off when Mr Peters told the crowd he had "made no agreement'' to speak.
He launched an angry tirade at Mr Peters, yelling: "If you lie, I will turn you off, you f*** ... now speak the truth.''
When Mr Peters was finally allowed to address the crowd, he told the crowd Mr Elliot was "not the national censor''.
He got loud cheers of agreement when he asked if the crowd believed in freedom of speech and the right to make their views heard.
Before the argument, the protesters heard from Green Party co-leader Russel Norman, Mana Party leader Hone Harawira, and Labour's state owned enterprises spokesman Clayton Cosgrove.
Asked afterwards why he initially declined to speak, Mr Peters said he was happy to talk to the protesters but he wanted to hear what they had to say first.
"When he (Mr Elliot) starts making up that sort of statement, I think it behoves us all to put him straight.''
Asked about yesterday's press release that said he would speak, Mr Peters said the party had always been opposed to asset sales.
"This is nothing new to us, it's not about talk, it's about action.''
Mr Elliot told APNZ that Mr Peters had agreed in an email to speak at the rally.
"When Winston's turn came to speak, I turned to him and offered him the chance to speak. He declined,'' he said.
"At the end, Winston came over and decided he did want to speak. Now I was not sure whether the crowd was any longer wanting to hear what Winston had to say, so I put it to the crowd.
'They did want him to speak so I gave him the microphone. He then proceeded to tell lies. He said that he had never agreed to speak to this group - that was a lie.''
Occupy Wellington announced the rally in a press release on Saturday that said speakers from New Zealand First, Labour and the Greens would be present.
But organisers seem to have given political parties little heads-up, with some parties named in the press release having scant details in the hours before the rally.
A Green Party spokesman said he was unaware what time the rally would start and would "look out the window'' to see, while a Labour spokeswoman said it was still undecided who would speak at the rally.
The Speaker's Office said protest organisers had not contacted the office ahead of the rally, but because no other groups were booked in to use Parliament's ground, the protest would be allowed to go ahead.
Asked about the apparent lack of organisation, Mr Elliot said the protest had been organised in very little time.
"Given the tight time-frame I'm very happy with everything that happened here today. The fact that we've had the leaders or senior members of most significant political parties speaking here today, I think that speaks volumes.''
Asked if he had not let political parties know, Mr Elliot said: "If anyone is disorganised, it is not us.''
