The completion date for cleanup of contaminated construction and demolition debris dumped three years ago on a Central Islip property was set for June 27 by a judge overseeing the case.

Attorneys for Thomas Datre Jr. and Christopher Grabe, who pleaded guilty to dumping crimes on March 31, and Tommy Lau, who owns the 1-acre plot on Islip Avenue, met in state Supreme Court Justice Fernando Camacho’s chambers Friday morning along with prosecutors for what Camacho called “an extensive conference.”

“Things are in place to begin that cleanup and it’s expected to be completed by June 27,” Camacho said in open court. “We have a plan to be able to do that.”

“We are hopeful we can meet that date,” Lau’s attorney, Michael White of Westbury, replied.

Earlier this week, Camacho asked prosecutors to invite a state Department of Environmental Conservation official to join in on the conference. A representative for the DEC was not in court Friday, but White said the agency sent a letter to Camacho indicating its cooperation with the cleanup efforts. A request for comment from the DEC went unanswered.

White said outside court he had been working with the DEC to “present a couple of alternatives that might be faster and more cost-effective to Mr. Lau.” White would not elaborate on what those alternatives might be. Camacho has said the state agency approved the remediation plan, which was supposed to begin during the last week in April.

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“It’s just a question of coordinating resources and making sure we have the proper oversight by the DEC,” Kevin Kearon of Garden City, Datre Jr.’s attorney, said. “The DEC needs to have monitors present. We are cooperating with the DEC in making sure that we follow all of their instructions.”

Several months ago Lau removed about 1,200 tons of materials from the site and trucked them to an approved out-of-state facility, White has said.

On Friday, the piles of debris — some seemingly untouched since authorities discovered them as high as 30 feet two years ago — were covered in green vegetation. Inside the fenced-in lot was a payloader, an excavator, cesspool rings and a concrete crusher, with one small yellow sign on the fence: “Caution: Hazardous material storage area.”

Thomas Datre Jr. pleaded guilty to four felony counts of endangering the public health, safety or the environment in connection with illegally dumping debris laced with toxins at four Suffolk sites: the Central Islip lot; Roberto Clemente Park in Brentwood; a sensitive wetlands area in Deer Park; and a six-home development in Islandia built for returning Iraq and Afghanistan war veterans and their families.

The guilty plea came in the sixth week of a criminal trial against Datre Jr. and his father, Thomas Datre Sr., near the end of the prosecution’s case. Charges against Thomas Datre Sr. were dropped as part of Datre Jr.’s deal. Grabe, of Islandia Recycling, was not on trial at the time but also pleaded guilty to two felonies related to the dumping, as well as a separate charge for tax evasion.

Camacho deferred prison sentences for Thomas Datre Jr. and Grabe to allow them to fulfill a condition of their guilty pleas, which requires that they both use their time and equipment to help clean up the remaining contaminated sites as well as to help rehabilitate Clemente Park, the largest public park in the heavily minority-populated hamlet.

Although Islip Town last summer removed contaminated material from Clemente Park, it still sits shuttered and dilapidated. Several rounds of cleanup work at the Islandia site were done over the past two years by the Long Island Home Builders Care Development Corp., the charitable arm of the Long Island Builders Institute, which constructed the homes there.

Camacho instructed the defendants’ attorneys to work with the DEC to come up with a plan for the wetlands site, and said he would continue to hold “regular” conferences to discuss the progress of the different remediations, “and we’ll do that for as long as it takes.”

Three other men named in the dumping indictment have cases pending before the court, including former Islip Town parks Commissioner Joseph J. Montuori Jr. and his former secretary, Brett A. Robinson. Jury selection in the case against Ronald Cianciulli, the owner of Atlas Asphalt charged with helping facilitate the dumping at the wetlands site, is set to begin next week.