Police detained Father Frank Bwalya in Kitwe while he was on air for the Roman Catholic church-owned Radio Icengelo.
Hundreds of his supporters marched through the town - an opposition stronghold - demanding his release.
After he was freed on a police bond he went on air to appeal for calm, but he said he would continue his campaign.
The BBC's Boyd Chibale in Kitwe says the priest had been running a programme analysing the conduct of the presidential poll and the pattern of the results.
President Rupiah Banda of the Movement for Multi-Party Democracy narrowly won last month's election, which was declared free and fair by African regional election observers.
But opposition leader Michael Sata of the Patriotic Front has claimed it was rigged, and has demanded that the results be verified.
Father Bwalya told the crowd that had gathered outside the police headquarters in Kitwe that he had been "charged for allegedly making statements that have the potential to cause hostility between communities or groups in the country".
"I've also been alleged of having said that the elections we just had on 30 October were fraudulent and that current president was not legitimately elected," he said.
"I'm innocent until proven guilty. The matter will go to court... on 27 November."
Our reporter says earlier in the day hundreds of people supporting Father Bwalye - an influential figure in the town - had brought Kitwe to a standstill and many shops were closed for fear of riots.
Taxis and buses were tooting their horns and protesters in the crowd chanted: "We want change".+++++++++++++++++++++++++++++++++++++++++++++++++++
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(Source: BBC)