Mayor Lori Lightfoot may have her first 100 days and her initial “State of the City” address under her belt, but former mayoral rival Toni Preckwinkle is still getting under her skin.

The bad blood between the mayor and the Cook County Board president boiled over yet again on Friday in Lightfoot’s meeting with the Chicago Sun-Times Editorial Board — and Preckwinkle showed no signs of letting it go.

In the latest round of the seemingly never ending prize fight between the two most powerful women in Chicago, Lightfoot ripped into Preckwinkle for rebuffing her efforts to work together, saying “a lot of that is up to her.”

But Preckwinkle fired back that she has sought to meet with Lightfoot and her top cop to discuss solutions to Chicago’s street violence, but to no avail.

“Talking about collaborating and demonstrating the leadership to do so are two different things,” Preckwinkle said in a statement she fired off after Lightfoot’s latest jab.

The mayor reopened the old wound on Friday, acknowledging that she was “stepping into some hot water” when she brought up a letter she received from her former campaign rival in July.

She jumped in anyway.

“Let me be clear, I have said ‘Madame president, chief judge, sheriff, state’s attorney, let’s get together, let’s put our data out for the public to be able to see it and let’s work together towards solutions’ and what I got back was not a ‘yeah, that’s a great idea.’ I got back another nasty-gram from her,” Lightfoot said.

“So other people who are part of this ecosystem have reached out and said let’s have a conversation and I commend the chief judge and the presiding judge and Sheriff [Tom] Dart and State’s Attorney Kim Foxx because I think all of us can … make some progress. And we will make progress.”

At the center of the battle is Preckwinkle’s argument that her bail reform efforts have no connection to Chicago’s problem of street violence.

In a statement released to the Chicago Sun-Times Friday, Preckwinkle touted the county’s “significant strides in reforming Cook County’s criminal justice system” and said she and others know that bond reform hasn’t led to an increase in violent re-offenders.

“To say otherwise is a falsehood and nothing more than a fear tactic,” Preckwinkle’s statement goes on to say.

And Preckwinkle swatted aside claims that her arguments are driven by her failed mayoral run, saying “this is about governance — not politics. To say my concerns are in response to a long-gone election is their talking point and that still does not make it the truth.”

What Lightfoot dubbed the “ongoing tussle in the media” over bail reform stems from a July letter Preckwinkle sent to Lightfoot, complaining that the mayor and Chicago Police Supt. Eddie Johnson were promoting a “false narrative” that portrays the county’s bail reform efforts as “the root cause for gun violence.”

The mayor said Friday the issue isn’t about bail reform but about not “returning people to the streets who are wreaking havoc in neighborhoods.”

Lightfoot said she had no inkling that the July letter was coming, even though it would’ve been easy for Preckwinkle to give her a heads up. The two met the week before the letter was released and “outlined a number of ways in which I thought we could work together productively on things that are important to both the city and the county,” Lightfoot said.

“But some things are clearly more important to her than others,” the mayor said Friday.

Since then, Lightfoot says she’s met with many of the county elected officials on the topic of bail reform though not with the board president.

In her response, Preckwinkle said Lightfoot has no one to blame but herself.

“Here are the facts: We’ve invited the Mayor and Superintendent Johnson to the table several times in hopes of having a productive conversation based on identifying solutions,” Preckwinkle said. “It is clear they are not willing to sit down as they have either been unavailable or declined those requests.”

Preckwinkle and Lightfoot have presented different statistics to back up their differing claims on bail reform and its role in street violence.

They have had zero personal follow-up conversations about the letter or how to leverage their resources and work together.

Lightfoot admits she hasn’t reached out to Preckwinkle.

When asked if the County Board president has reached out to her, Lightfoot said, “not that I recall.

“I think there’s been some — I hesitate to call them communications — but there have been some conversation at the staff level.”

Despite the two being estranged, Lightfoot doesn’t think it will impede the city’s ability to “get done what needs to get done” though “a good strong constructive relationship would absolutely be to the benefit of people in this county.”

But Lightfoot added “a lot of that is up to her.”

“If President Preckwinkle is interested in having a productive conversation on any topic my door is always open,” Lightfoot said.