"It's definitely not the outcome that we wanted, obviously," Abben said, appearing to fight back tears during a news conference in Evansdale. "This is a difficult thing for us to go through. It's a difficult thing for the community."
He said the bodies were being sent to the state medical examiner's office to confirm their identities.
A vigil was being held Wednesday night for the girls at the lake.
Hundreds of volunteers had helped investigators search for the girls after they went missing, traipsing through cornfields and wooded areas in and around Evansdale, a city of 8,000 residents. The mayor even flew above in his private plane looking for them.
Days later, an FBI dive team brought in specialized equipment to search the bottom of the lake for the girls but found nothing. Police then classified the case as an abduction.
Investigators had largely been tight-lipped in the months since. An FBI spokeswoman initially said investigators had reason to believe the girls were alive, raising the region's hopes. But other investigators backtracked, saying only that there was no reason to believe the girls were dead.
Authorities had asked hunters to look for the girls in the region during this fall's popular deer hunting season.
Abben said the bodies were discovered around 12:45 p.m. Wednesday, but refused to say where, saying the area was still being processed as a crime scene and could not be compromised.
"Preservation of that scene is paramount," he said.
Abben said he hoped to release additional details Thursday.
Abben said the girls' families wanted to express gratitude to the community for their support but have asked the media to respect their privacy at this time.
Investigators have poured through thousands of tips and chased many different theories in the case.
They looked into Cook's parents, who had criminal records for prior involvement in making methamphetamine. Cook's father, Daniel Morrissey, is being prosecuted for domestic assault and a series of meth and other drug charges, and he backed out of a plea agreement with prosecutors the day before the disappearance. They have denied any involvement.
The region had rallied in support of the girls. Photographs of the cousins seemed to be everywhere in northeastern Iowa: on T-shirts and buttons worn by locals, and on fliers hung on gas station walls and in business windows.
Local residents held repeated prayer vigils for the girls and their families, even as days passed and both girls had birthdays. Just last week, an anonymous donor pledged $100,000 for information about the girls' whereabouts, on top of the $50,000 that police had offered.