ORLANDO, Fla. -- The grandmother of a 2-year-old girl missing since early June said Monday the girl's mother, jailed after police said she failed to report the disappearance for more than a month, knows who has the toddler.

A lawyer for the Orlando girl's mother, Casey Anthony, said his client wants to help investigators and urged authorities to release her.

Anthony, 22, was arrested last week after telling authorities her daughter Caylee Marie Anthony had been missing since June 9. Casey Anthony was charged with child neglect and criminal obstruction for allegedly lying to detectives.

Her mother, Cindy Anthony, said Monday on NBC's "Today" her daughter should be released so she can help detectives.

"I know Casey knows who has her," she said. "I know Casey doesn't know where they're at right at the moment. But I don't know anything else right now because I can't speak to my daughter. And we're trying to get that changed very quickly."

Casey Anthony's lawyer, Jose Baez, said his client wants to cooperate with authorities.

"She is a good mother and has no history of being a bad mother," Baez said. "She wants to find her daughter."

Baez said Anthony doesn't know where the girl is, but he was sending investigators a letter pledging her cooperation.

Sheriff's officials say Anthony has repeatedly lied to them and showed little emotion or concern in interviews just before her arrest.

Orange County Sheriff's deputy Carlos Padilla said Baez hasn't returned detectives' calls to set up a meeting.

"The key lies in the mother, and we would hope the lawyer would allow the detectives to speak to her in his presence to find out exactly where this child is," Padilla said. "This lawyer has taken the time to take this to the media, but he's not yet returned the phone calls to discuss this."

Anthony is being held without bail and scheduled in court Tuesday.

Padilla urged the person who might have the girl but is worried about being prosecuted to drop her off at a hospital or law enforcement office.

Last week, investigators used cadaver-sniffing dogs and dug through Cindy Anthony's backyard looking for the toddler. Detectives say Casey Anthony asked a neighbor to borrow a shovel around the time her daughter went missing.

They said she contacted police last week because the girl's grandmother was concerned.

Anthony told detectives she didn't call authorities immediately because she was conducting her own investigation, according to the charging affidavit. The apartment where she said she dropped off the girl hadn't been occupied in months, and Casey Anthony gave detectives a bogus employer, manager's name and work telephone number, according to the affidavit.