Sean and Ryan Esmond and their parents fell ill after an applicator working for Terminix used methyl bromide at the resort in the U.S. Virgin Islands.
The teens are hospitalized in Philadelphia. Their father and mother, Stephen Esmond and Theresa Devine, continue to undergo therapy, said the family's statement, which provided the first update on the family's medical condition in a month.
"The Esmond Family thanks the nation for its outpouring of support and concern for the family's recovery from this unthinkable tragedy of pesticide poisoning during their family vacation," the statement said.
The Environmental Protection Agency, the Department of Justice and authorities in Puerto Rico and the Virgin Islands are investigating.
The EPA said in April that its probe had found the toxic pesticide was used at the Sirenusa Condominium Resort in St. John several times in the past and may have improperly been used in Puerto Rico. The agency banned the chemical for residential use in 1984.
"The family is confident that those responsible will be brought to justice," the Esmonds' statement said.
Stephen Esmond is head of a private middle school in Wilmington, Delaware, and Devine is a dentist in the Philadelphia suburbs. The family had travelled to the Virgin Islands for vacation with several other families from Wilmington's private Tatnall School.
Methyl bromide, an odourless and highly toxic gas, can severely damage the lungs and brain. The chemical was applied to a vacant unit directly beneath the Esmonds' unit at the posh resort overlooking Cruz Bay, environmental regulators say.
The teenagers' prognosis depends on how long they were exposed and how much they breathed in, said Dr. Reynold Panettieri, deputy director of the Center of Excellence in Environmental Toxicology at the University of Pennsylvania's medical school.
"The potential for meaningful recovery is still there," Panettieri, who is not involved in the teens' care, said recently. "As you get farther and farther out, the potential for meaningful survival and living independently is going to become less and less likely."
Terminix, the Memphis, Tennessee-based pest-control firm, said Monday it is co-operating with investigators and conducting its own internal inquiry. The company added it has halted all fumigation operations in the U.S. Virgin Islands and reinforced its policies and procedures with all employees.
The Virgin Islands' Department of Planning and Natural Resources has suspended the Terminix applicator's license.
Associated Press writer Ben Fox in Miami contributed to this report.