Police have said civilians and security forces have been killed as soldiers battle the defenders of a powerful gang leader.
Christopher Coke, known as "Dudus", is wanted by the US for alleged drug offences.
Heavily armed soldiers and police have conducted door-to-door searches in the hunt for him in the Tivoli Gardens neighbourhood of West Kingston.
Coke has not been found and there are some reports he could have left the island.
Jamaican Prime Minister Bruce Golding has said he "regrets the loss of life" and has vowed to restore law and order in the Caribbean nation.
Christopher 'Dudus' Coke
The searches and reports of sporadic gunfire, came a day after a full-scale military assault on the slum where Coke was believed to be hiding out.
Two trucks brought in "about 50" bodies early Tuesday to the morgue at the Kingston Public Hospital, a nurse told AFP.
An AFP correspondent witnessed a third truck arrive outside the morgue in the afternoon piled with corpses riddled with bullet wounds, including a baby.
Today masked gunmen in West Kingston vanished down side streets barricaded with barbed wire and junked cars intended to block outsiders.
There have been reports of gunfire echoing across neighbourhoods in Jamaica's south coast, far from the all-inclusive tourist meccas of the north shore.
In a separate incident, armed gangs attacked police outside one of the main hospitals in the Jamaican capital, forcing medical staff to close the building's doors.
The gun battles erupted when gang members tried to go inside the Kingston Public Hospital to accompany about 20 corpses killed in Monday's assault, but were barred from entry by the staff.
A state of emergency has been declared in parts of the capital.
A police station in Kingston is set on fire
Violence erupted on Sunday after nearly a week of rising tensions over the possible extradition of Coke to the US, where he could face a sentence of life in prison.
He leads one of the gangs that control politicised slums known as "garrisons."
Political parties created the gangs in the 1970s to rustle up votes.
The gangs have since turned to drug trafficking, but each remains closely tied to a political party. Coke's gang is linked to the governing Labour Party.
The US State Department said it was "the responsibility of the Jamaican government to locate and arrest Mr Coke."
A US Embassy spokeswoman denied widespread rumours that US officials had been due to meet Coke's lawyers.
Source : http://news.sky.com/skynews/Home/World-News/Jamaica-At-Least-31-People-Die-In-Battles-Between-Police-And-A-Drug-Gang/Article/201005415638239?lpos=World_News_Carousel_Region_3&lid=ARTICLE_15638239_Jamaica%3A_At_Least_31_People_Die_In_Battles_Between_Police_And_A_Drug_Gang