Jamaican security forces are fighting with gunmen as the government attempts to take control of an alleged drug lord's stronghold in the capital.
Gunfire erupted as troops and police stormed the Tivoli Gardens area to search for Christopher "Dudus" Coke, who is wanted in the US.
A soldier was killed. It follows two police deaths on Sunday.
Supporters of Mr Coke are fighting to stop his extradition to the US on drug and gun-running charges.
So far there is no indication that the security forces have been successful in tracking down their target in the warren-like slum.
Gunmen in the area are reported to be heavily armed. There are unconfirmed reports of civilian victims.
Mr Coke, who insists he is a legitimate businessman, enjoys the support of many impoverished Kingston residents who see him as a benefactor and have vowed to protect him at any cost.
There are also reports of violence in other parts of the capital, raising fears that the unrest is spreading.
A state of emergency remains in place in parts of Kingston.
The restrictions were imposed on Friday after several police stations were attacked following an announcement by the prime minister agreeing to the extradition of Mr Coke.
The BBC's Nick Davis in Kingston says the operation started about noon on Monday, when large numbers of soldiers were seen heading to the poor Tivoli Gardens area.
Plumes of smoke could be seen coming from the area as helicopters buzzed overhead.
Security Minister Dwight Nelson said the soldiers, in a joint operation with police, had broken down the barricades around Tivoli Gardens and were conducting a house-to-house search for Mr Coke.
"The purpose of the operation is to execute the warrant for extradition and to detain [Coke] so he can appear in court," he told the BBC.
He insisted the police were "doing everything in their power to ensure the city remains safe".
But some reports said police had met heavy resistance from gunmen as they tried to enter Tivoli Gardens.
Residents in the area were advised to remain indoors but the streets were already quiet as Jamaica observed its Labour Day holiday.
The US State Department said the fighting had intermittently blocked the road to Kingston's international airport and forced the cancellation of some flights.
Tivoli Gardens, the constituency represented in parliament by Prime Minister Bruce Golding, is the stronghold of Mr Coke, 41, who describes himself as a community leader.
His supporters see him as a man who is fulfilling a role that the government does not, such as giving them money to support their children.
Before the fighting, they staged protests and barricaded streets to stop his arrest and extradition.
One resident of Kingston, Suzanne, rang the BBC to say Mr Coke provided a valuable service to the community - unlike the politicians.
"If your grandmother dies, you go to him and he buries her," she said.
"Okay, that's a fact. If you're a politician you're not going to find him, especially Bruce [Golding], you're not going to find him anywhere in the constituency, so you go to him [Dudus].
"You need your child to go to school - you go to him, and this is how it's been, this kind of patronage."
The US justice department accuses Mr Coke of being one of the world's most dangerous drug barons.
He is said to lead a gang called the Shower Posse - owing to the volume of bullets used in shootings - and operate an international smuggling network.
He faces a life sentence if convicted on charges filed against him in New York.
The gang has also been blamed for numerous murders in Jamaica and the US.
The trouble started last week when Mr Golding said he was prepared to send Mr Coke to the US on drugs and weapons trafficking charges.
The decision reversed nine months of opposition to his extradition.
Mr Golding had argued that the evidence against Mr Coke was obtained illegally by intercepting mobile telephone calls.
But he changed his mind in the face of growing public discontent, and questions about his possible ties to Mr Coke.
He has denounced the unrest as a "calculated assault on the authority of the state that cannot be tolerated".