Government chief whip Andrew Mitchell has faced renewed calls to resign after a "wasted" meeting with Police Federation officials over his rant at officers in Downing Street.

The embattled MP repeated his profound apology over the "Plebgate" row during a 45-minute discussion with representatives of the West Mercia, West Midlands and Warwickshire police federations on Friday.

But Mr Mitchell again refused to confirm what he said to officers in Downing Street, sparking calls for his resignation from Ken Mackaill, chairman of the West Mercia federation.

"He is continuing to refuse to elaborate on what happened and I think his position is untenable," Mr Mackaill said as he emerged from the meeting in Mr Mitchell's Sutton Coldfield constituency.

Speaking at the rear of Mr Mitchell's constituency office, Mr Mackaill described the talks as a "wasted meeting in that we are no further down the road", but said he appreciated the chance to put his concerns directly to the MP.

The police federation official added: "Unfortunately he's not had anything new to tell us. Whilst he has repeated his - to use his words - profound apology for what he did say ... he has also repeated his denial of using many of the words reported in the officers' notes recorded at the time. I think Mr Mitchell now has no option but to resign."

While he had given an apology for his altercation over a refusal to allow him to cycle through Downing Street's main gate, Mr Mitchell continued to dispute the officers' report that he called them "plebs", Mr Mackaill said. "He refused to tell us what he did say on the grounds he did not want to impugn police officers' integrity. Unfortunately that is exactly what happened: the question of integrity remains unresolved."

Mr Mackaill, who was accompanied at the meeting by the secretaries of the West Midlands and Warwickshire federations, said integrity is a massive issue among rank-and-file officers. "This is about the honesty and accuracy of police records and there are implications for officers giving evidence in court, after all. We take the view that this is a Cabinet minister challenging the accuracy of police records and that, we think, is of interest to all police officers."

Mr Mitchell left without making comment amid pressure on Prime Minister David Cameron to sack him, weeks after appointing him to the key position in the reshuffle. The Cabinet member did not attend this week's Conservative Party conference amid speculation that he could lose his job.

Defence Secretary Phillip Hammond said the row over Mr Mitchell's outburst had been "hijacked". Mr Hammond told the BBC the Police Federation was using the situation as an excuse to bring up its own issues and grievances. He told Radio 4's Any Questions: "We've now got other people who were not involved in the incident who seem to be trying to hijack this issue now and take it forward for their own purposes. The man's apologised, the person he insulted has accepted the apology, let's draw a line."