UPDATED 01/27/12 6 p.m.

CHICAGO (CBS) — Some Chicago clergy members tried to gain access to the over-flowing body storage cooler at the Cook County morgue this morning to pray.

As CBS 2’s Susanna Song and WBBM Newsradio’s Mike Krauser report, the pastors intended to go inside the morgue, 2121 W. Harrison St., and pray over the indigent bodies. But, the Medical Examiner’s office did not allow them inside. Instead, they prayed in the lobby.

LISTEN: WBBM Newsradio’s Steve Miller Reports

LISTEN: WBBM Newsradio’s Mike Krauser Reports

The pastors are also calling for a meeting with Cook County Board President Toni Preckwinkle.

They gathered outside the morgue at 9 a.m. Friday. Their main focus, aside from praying is to ask the County Board if they, as clergy members, can oversee the work that is done in the morgue to ensure all unclaimed bodies are properly buried or cremated.

The pastors are calling for an independent oversight board comprised of religious and community leaders. And they are calling the current situation a national embarrassment.

On Thursday, Preckwinkle promised to overhaul the Medical Examiner’s office and fire some workers, after finding bodies stacked up in blue bags outside a full cooler.

Last week, 363 bodies were stored in a cooler designed to hold only 300 bodies.

“We are appalled by the situation happening here that has been revealed. We feel that it is a disgrace to our city and to our county to have such a situation on our hands,” said the Pastor Cy Fields of New Landmark Baptist Church. “We believe that there not only should be in dignity in living, but also dignity in death.”

“Regardless of the financial conditions of individuals when they die, every person is entitled to a decent burial,” said Bishop James Wilkowski of the Evangelical Catholic Church.

The pastors say the concerns they are raising are not new.

“We brought this up, really, over six months ago,” said the Rev. Marshall Hatch of the New Mount Pilgrim Missionary Baptist Church. “We knew once the state funding was cut off, that poor people were going to have a problem claiming the bodies of their loved ones. If they could not afford a funeral, the body could only be here at the morgue.”

“I’m truly saddened by the fact that so many persons’ bodies are just laying here, and what I’m hoping that the outcome of this would be is that, number one, it gets corrected and gets turned around; that some mechanisms will be put in place to ensure that this sort of thing won’t happen again,” added the Rev. David Pope of the Brotherly Love Church in Lawndale.

As ministers prayed outside of the morgue, investigators from the Illinois Department of Labor began an investigation inside.

Labor Department spokesperson Anjelia Julka said the investigation began Thursday, after it received a complaint alleging unsafe conditions.

Julka refused to be specific about the nature of the complaint, who complained or how many employees of the Medical Examiner’s office are expected to be questioned. It was received earlier this month.

She said that in the past two years, the agency has received five complaints about conditions at the morgue.

While some people will be let go, Chief Medical Examiner Dr. Nancy Jones will stay on the job for now, Preckwinkle said.

Preckwinkle said the morgue would have daily inspections of the overstuffed cooler, and new technology will be used to help track down relatives of the dead who are brought to the office in order to speed up the burial process.

Senior management at the morgue will be reorganized and new management positions will be created, according to Preckwinkle.

She also said the morgue will place time limits on how long the bodies of indigent people can be stored in the cooler, as well as how long the morgue will keep remains for families trying to collect enough money for a burial. The county will also put in place new training standards for the staff, as well as a new disciplinary process.

Reports of the deplorable conditions at the morgue have been making headlines for weeks. WBBM Newsradio’s Steve Miller reported earlier this week that 44 bodies have been found in the morgue for 10 months or longer, awaiting burial.

When the Chicago Sun-Times first broke the story about problems at the morgue more than a week ago, Dr. Jones said “yes, we do” have a larger than normal number of bodies at the office. But she said there were about 300 bodies there, not the 400 adults and 100 fetuses one source told the Sun-Times were in the cooler.

Dr. Jones has blamed state funding cuts as one reason for the body backlog and other problems at the morgue.

Preckwinkle admits that staffing shortages are partially to blame.

Now, a proposed county ordinance could make it easier for the board to remove a Medical Examiner. County Commissioner John Fritchey (D-12th) is the sponsor.

“This legislation is not directed at Dr. Jones,” Fritchey said. “The present county policy is bad public policy.”

Preckwinkle expressed agreement with the idea.

“I think, frankly, inappropriate for anybody in county government to have a term that’s equivalent to a federal judge, which is a life term,” she said.

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