Kenya's human rights commissioner has criticised conditions at Meru jail, where seven prisoners have died.
Ulcerated wounds could afflict those standing for a long time, Mr Kitur said
After a tour of the prison, Tirop Kitur said many of the inmates had open wounds because of the cramped conditions and poor ventilation.
Prison officials say the prisoners who died suffocated in a cell the size of a single bed. Police are investigating scars on five of the bodies.
Another 28 inmates are in hospital in a critical condition, Mr Kitur said.
"In fact we fear a number of others will die soon," Commissioner Kitur told the BBC's Focus on Africa programme.
Mr Kitur said investigators were still trying to establish the cause of deaths, which have risen from five to seven since Monday, but he said overcrowding was the "main problem".
Kenya's Vice-President Moody Awori, who is in charge of prison reform, said if allegations that prisoners were beaten by wardens were true, the culprits would be punished, the AFP news agency reports.
"If any of those people could have died as a result of having been beaten by any of the wardens... [the wardens] will face severe disciplinary action," Mr Awori told reporters in the capital Nairobi.
The prison in north-eastern Kenya was designed to house 500 prisoners, but is holding more than 1,400 inmates.
"A cell that's supposed to have 100 prisoners is having 300," Mr Kitur said.
As well as open wounds, Mr Kitur said some prisoners had swollen feet - all indications of standing for long periods of time with no exercise.
According to the prisoners questioned during the visit on Tuesday, the only exercise is when they are allowed out of their cell for meals, approximately 30 minutes a day.
"They're dirty. They're not healthy human beings. They don't have enough exercise... and the food is not adequate," Mr Kitur said.
Most of the inmates in Meru prison were on remand for petty offences, waiting for their cases to be heard, Mr Kitur said.
"Many of them have stayed there for a long time... the delays are inordinate," he said.
According to a recent report by Amnesty International, hundreds of Kenyans die in prison every year, some as a result of torture and some from infectious diseases caused by overcrowding.