Judge Raghib Hasan accused the men of killing an Iraqi policeman and wounding another, carrying unlicensed weapons and holding false identification, said Qasim al-Sabti, the head of the lawyers syndicate in the southern city, on Saturday.
Britain's Ministry of Defence said on Saturday the warrants had no legal basis.
"All British troops in Iraq come under the jurisdiction of Britain," a defence spokesman said in London.
The whereabouts of the two soldiers was not clear.
British forces mounted a bid to free the two soldiers on Monday by surrounding the police station where they were being held with several tanks and armoured vehicles.
But a crowd quickly gathered, angered by the death of the Iraqi policeman.
Five Iraqi civilians were killed and three British soldiers were wounded as the crowd threw petrol-bombs at armoured vehicles.
Basra authorities had said British troops also killed two Iraqi policemen during the raid.
Later, British forces returned and armoured vehicles flattened cars parked nearby as they broke down the walls of the police station and jail.
Iraqi police said the police station
was destroyed in the British attack
Iraqi authorities said the jail and the police station were demolished.
The two soldiers were later freed from a private house nearby, where British military authorities believed they were being held by a local militia.
Monday's flare-up has harmed the relationship British forces were able to build with local Iraqis in and around Basra, a relatively stable city compared with other parts of Iraq.
Officials said the Basra's governing council stopped all cooperation with the British until they apologise, guarantee that similar actions are not taken again and provide compensation for the damage inflicted during the operation.
An investigation into the events leading up to the rescue is under way by Iraqi authorities and the British military.
"We will continue to work closely with the Iraqis and the inquiry which the Iraq government has begun into the events of Monday," the British defence spokesman said.
Britain's secretary of defence said he stood by the actions of the forces on the ground.
"They did what they judged was appropriate at the time and I commend them for the swift and decisive action in very difficult circumstances," John Reid said.