Basra's governor has threatened to suspend dealings with UK forces unless five police officers being held as suspected insurgents are released.
The operation targeted police corruption, the British say
The men were arrested on Tuesday in a British-led operation following an increase in roadside bombings.
British officials said Iraq's Interior Ministry ordered the arrests and local officials were aware of the move.
But Mohammed al-Waili has called for a protest on Sunday outside the British consulate in the southern Iraqi city.
The governor said the city's provincial council and all government offices "will suspend all kinds of dealings with the forces at all levels if they don't release the detainees".
Fourteen men were arrested on Tuesday as part of drive "to root out corruption in the Iraqi police service", British military officials said.
Nine were later released after the operation involving British and Danish troops.
The Ministry of Defence said those being held are suspected of links to the kidnapping and assassination of Iraqis, as well as attacks on police and the multi-national forces.
On Wednesday, several hundred Iraqis held a demonstration outside the governor's office demanding the release of the detainees.
In October, Mr al-Waili said British forces had destabilised security following the arrest of 12 people over attacks against UK troops.
He said at the time the British should have co-ordinated the move with him and Iraqi security forces.
A month earlier, he had accused the army of "aggression" after the rescue of two British soldiers held by militias.