Wilkowski was among a group of clergy Friday who were denied entry to view the morgue.
"No matter how gruesome and upsetting the situation is, we need to open the doors," Wilkowski said. "I would equate that with an abusive spouse who says, 'You can't see my wife until after she heals from the wounds that I've inflicted upon her.'"
At an appearance at the Chicago Outdoor Sportsmen Show in Rosemont Saturday, Preckwinkle said she had not yet read Wilkowski's letter, but offered a timeline for turning the morgue around.
"I'm hopeful that we will be able over the next several weeks to get a handle on things there," she said. "We found ourselves this fall and more recently over capacity, but that doesn't mean we were disrespectful of the remains of the deceased."
Wilkowski and other clergy have stopped short of calling for the firing of medical examiner Dr. Nancy Jones.
Earlier this week, Preckwinkle said Jones would continue as ME, but Saturday offered more measured comments.
"Dr. Jones is the medical examiner," she said. "There's an administrative staff there. We're going to look at everything top to bottom and take whatever corrective action we think is appropriate."
In the last week, ABC7 has spoken to at least two families whose missing loved ones turned up at the morgue after officials for months said they weren't there.
The great aunt of Tionda and Diamond Bradley, who have been missing since 2001 said the word of morgue officials now to her means nothing.
"For all we know Stacy Peterson could be over there," said Shelia Bradley-Smith. "We don't know. And how can i be sure that Tionda and Diamond are not there?"