The decision to stage the pay rise has infuriated officers
The Police Federation has offered what it calls an "olive branch" to the home secretary in the bitter row over pay.
The federation had called for Jacqui Smith to resign over her decision not to backdate a 2.5% pay rise for police in England, Wales and Northern Ireland.
But in a letter, its chairman Jan Berry now says she believes Ms Smith was badly advised, although she urges her once again to reconsider her decision.
Ministers say the award is appropriate and is in line with inflation targets.
'Angry and disappointed'
The decision not to backdate to September the 2.5% pay rise agreed at arbitration has outraged police officers.
Officers say this amounts in real terms - taking into account inflation - to an increase of 1.9%.
It has prompted the Police Federation to say it will ballot members in 2008 on whether they want the right to strike.
Police officers across the UK are currently banned from taking industrial action.
In her open letter to the home secretary, Mrs Berry, who chairs the Police Federation of England and Wales, warned that officers remained "angry and bitterly disappointed" at the pay settlement.
But she said she believed Ms Smith had been the victim of ill-informed and naive counsel in her early weeks in office and that it was not too late to reconsider the pay decision.
"I want to take this opportunity to offer an olive branch," she wrote.
"It's not too late to change course and stop this situation escalating."
Mrs Berry added: "You know the mood of police officers, the public and many of your political colleagues. I can assure you, we have no intention of letting this go.
"I would ask you therefore to urgently reconsider the decision. Do the right thing for policing, for police officers and for the good of the country."
Mrs Berry said such a move would "restore honour" in the office of home secretary and rebuild trust with officers.
The police's 2.5% pay deal was decided through the independent Police Arbitration Tribunal.
Mrs Berry wants to rebuild trust between ministers and officers
But while officers in Scotland are having their 2.5% pay rise backdated to 1 September, as the tribunal recommended, those in other areas of the UK received the rise this month.
Ms Smith's stance has been attacked by several police leaders, including Metropolitan Police commissioner Sir Ian Blair, who said she had made a "mistake" in refusing to meet police pay demands, although he did not believe she should resign.
The Home Office said Ms Smith would meet Mrs Berry in January to continue talks and try to find a "constructive way forward".
"The police pay award is higher than the original government offer and is now in police pay packets in full," a spokeswoman said.
"However, staging the award from December ensures that it is fair to both police officers and to other public sector workers, and is right for the future of our economy."
Keith Vaz, Labour chairman of the Commons home affairs select committee, welcomed Mrs Berry's letter and urged Ms Smith to engage in talks with officers.
"We need a New Year's resolution from the home secretary to end the bitterness and move on," he added.