Jesse Jackson Jr. and Sandi Jackson on Friday agreed to mediate their sizzling divorce case and avoid a potentially sensational trial where allegations of “extramarital affairs” could be publicly detailed.

But even as the contentious case appeared to wind down in courtrooms in Chicago and in Washington, D.C., Jesse Jackson Jr. threw fuel on the fire, telling reporters in Chicago that something he found on the couple’s home computer led him to file for divorce.

The former congressman said “discoveries” he made in March 2016 on the computer while Sandi Jackson was in federal prison “make it impossible for the marriage to continue.”

He did not elaborate on what he found, but said he wants “non-distribution” of it to protect his children.

“What is important is the information that is no longer in my possession … was sent to various individuals over the course of this process,” Jesse Jackson said. “This case will remain alive until such time as all of this information by agreement is returned.”

As Jackson spoke to reporters at the Daley Center, Sandi Jackson was in a Washington D.C. court house where a judge set a June 1 status hearing for the couple to report their progress in mediation talks supervised by the D.C. Superior Court.

Extraneous court motions, including allegations of extramarital affairs that each might have had – subject to public disclosure – will be on hold pending the outcome of the dispute-resolution sessions.

However, the spicy assertions could come up in the private mediation talks.

During mediation, the Jacksons will sit in the same room during negotiations, with their lawyers and an independent mediator present.

The most pressing issues in the case that could be resolved through mediation, D.C. Superior Court Judge Robert Okun noted in a hearing on Friday morning are custody of the couple’s two children; child support; alimony, and the distribution of their property, which consists mainly of two residences in Washington and one in Chicago.

RELATED: Sun-Times archive on the Jackson divorce case

Okun signed orders stating Jackson will pay Sandi Jackson $1,200-a-month in alimony, starting on June 1; $1,529 -a-month in child support; a continuation of paying for private school tuition for the children, and maintaining the current health insurance coverage for the family.

Still to be resolved is a pending motion regarding the payment of attorney fees.

The lawyers for the couple disagreed during the hearing — which lasted under 15 minutes — on how long a trial would take if the mediation fails.

Sandi Jackson attorney Chandra Walker Holloway told the judge a trial could take up to eight days. Jackson’s lawyer, Ann Marie Jackson — no relation — said a trial would only need three days.

Former U.S. Rep. Jesse Jackson Jr. addresses the media after a divorce hearing at the Daley Center on Feb. 27, 2017. | Ashlee Rezin/Sun-Times file photo

Because of the potential of a time-consuming trial, Okun sent to the case to D.C. Superior Court Judge Craig Iscoe. Outside of court, Jackson, the attorney, was asked about the prospects of resolving the case before June 1. “I don’t know. . . . It would be wonderful. . . . I don’t know whether that is likely to happen or not,” Ann Marie Jackson said.

“The parties have a shared interest in resolving this,” adding that mediation saves money and will be “beneficial to the children.”

Holloway, Sandi Jackson’s lawyer, said going to mediation is moving “in the right direction,” noting that the couple was coming to the negotiating table on their own — without a judicial order.

Both Jacksons went to prison in staggered terms following their 2013 convictions tied to the looting of the congressman’s campaign fund. Sandi Jackson, the former Chicago 7th Ward alderman, is about halfway through her 200 hours of community services at a food bank called Martha’s Pantry chopping vegetables and baking muffins.

After the hearing in Washington, Sandi declined to comment, other than to reply to the question of what kind of muffins she was baking.

Said Sandi Jackson, “banana muffins.”

In Chicago, Jesse Jackson Jr. was more talkative.

Just after a judge entered an order to dismiss the divorce case Jesse Jackson Jr. filed in Cook County, the former congressman engaged in a wide-ranging discussion with reporters at the Daley Center in the Loop. Besides discussing the mysterious discovery he said he made last year, Jackson discussed the end of their year marriage.

“As I shared with everyone from the very outset of this case, for 30 years Sandra and I have both had our ups and downs and we’ve survived them all,” he said.

“I’ve taken responsibility for all of my shortcomings as a man and all of my actions including marital behavior [and] imperfections of which I’m not proud. Today in some measure, I say goodbye to nearly 30 years of friendship and 25 years of marriage.

“Some people will understand that as human we all fall down and can get back up and others will never understand. I cannot likely ever reach through to the latter but I’m trying my best to speak to the former. I feel like [I have] personally learned the lessons of what power and what hubris could bring. but it seems we all come to these places in our own time and perhaps others of us never will.”