Authorities investigating the disappearance of two young girls in Iowa said Saturday that they believe them to still be alive.

Lyric Cook, 10, and her cousin Elizabeth Collins, 8, were last seen by their grandmother more than a week ago when they left on a bike ride.

"We believe these girls are alive and we are not discouraged by the passage of time since their disappearance," FBI spokeswoman Sandy Breault told reporters in Evansdale, Iowa.

She declined to discuss exactly what evidence investigators might have that pushed them toward that conclusion. Breault said she believes someone knows something, and she urged anyone with information to step forward.

Grandmother: 'We will fight'

A $50,000 reward is being offered for information leading to the successful recovery of the girls and the prosecution of the person, or people, responsible, she said.

"Cooperation with law enforcement is the key factor in discovering the whereabouts of Lyric and Elizabeth. Unfortunately, in this case law enforcement has not received total cooperation from all family and close friends. It's important to note that the majority of the family has cooperated 100%," Breault said. "We believe there's someone out there and we would urge them to come forward."

Family of missing Iowa girls 'bracing for the worst, but hoping for the best'

The girls' bicycles and a purse were found near Meyers Lake hours after they were reported missing July 13.

A search of the 25-acre lake turned up nothing, and the FBI is confident the girls aren't in the lake, said Breault.

Authorities are now calling their disappearance an abduction.