ORLANDO, Florida (CNN) -- The grandparents of missing 2-year-old Caylee Anthony continue to stand by their daughter, who is accused of killing Caylee, an attorney said Monday.

Caylee Anthony, 2, has been missing since June in a case that has received national attention.

The lawyer's announcement came just hours before a source confirmed authorities discovered bones in the area where a body believed to be Caylee's was found last week. The bones were scattered in the dirt, perhaps by an animal, the source said.

Crime scene investigators were searching the area where the body was found and will continue searching through at least Wednesday, according to Commander Capt. Angelo Nieves with the Orange County Sheriff's Office.

Outside agencies, including the FBI, were helping the sheriff's office sift through the area "in order to make sure that no stone, no area, is left untouched where the child's remains were found," Nieves said.

"Significant finds have been made," he added. "At this point, we cannot identify what items have been recovered."

George and Cindy Anthony were "devastated" upon learning a toddler's corpse had been found near their Orlando, Florida, home, attorney Brad Conway said, but the couple is waiting for authorities to confirm the body's identity.

"They're not grieving yet, because they don't know whose body this is, but if it is identified as Caylee they're going to go through that grieving process privately, and when they're ready to speak, they will," Conway told reporters.

A utility worker discovered the remains in a plastic bag Thursday and alerted authorities. CNN affiliate WFTV-TV in Orlando reported the utility worker, a meter reader, picked up a bag at the site and a skull fell out. Listen to the disturbing 911 call »

Later that day, authorities searched the Anthonys' home and removed "a number of items," Conway said.

Authorities have said Casey Anthony, 22, waited about a month before telling her family Caylee was gone. Caylee's grandmother called police on July 15, saying her daughter would not tell her where Caylee was. See where remains were found »

The girl was 2 at the time of her disappearance.

The FBI is using DNA analysis to try and positively identify the remains, Conway said.

Though bureau spokesman Richard Kolko said Monday he did not know when tests would be complete, Conway said the FBI is likely to have results "within the next week."

"Everybody wants to make sure that there are no mistakes made, that the person responsible for this crime is held responsible for it and, if that happens to be Casey, a jury of her peers will have to make that decision after the state of Florida proves beyond a reasonable doubt," he said.

If the remains prove to be those of their granddaughter, the body would be released to the Anthonys "for proper and respectful burial," he said.

Conway described his clients as "good, honest, decent people that are getting publicity that they do not deserve."

Orange County Sheriff Office's spokesman Carlos Padilla said last week that authorities believe the remains are Caylee's because no other children have been reported missing in the area, the remains are consistent with a child Caylee's age and the remains were found near the grandparents' home.

Caylee and her mother had lived in the house with Caylee's grandparents, but Casey Anthony moved into an apartment at the time Caylee disappeared.

Casey Anthony faces charges including first-degree murder in Caylee's disappearance. If convicted, she could face a sentence of up to life in prison. Prosecutors said this month they would not seek the death penalty.

Casey Anthony's attorneys have insisted she is innocent.

After learning a corpse was found last week, attorneys sought a court order allowing them to observe the autopsy and conduct their own forensic tests.

A judge denied the request after prosecutors said the motion was premature because the body had not yet been identified. Watch why police think it's Caylee »

"What I don't want to see, bluntly, is 24 hours after viewing an autopsy, a defense expert on a national news show describing this child's remains," prosecutor Jeff Ashton argued. "The specter of that is nauseating to me."

Asked Friday how Casey Anthony responded to the news her daughter's remains may have been found, lawyer Jose Baez said, "It's not something that someone takes well."

Casey Anthony remains in protective custody and has no contact with other inmates, corrections officials said. A psychologist has seen her, and she is on psychological observation, which is not the same as suicide watch, according to a statement.

Casey Anthony's trial, originally set for January, has been postponed until at least March.

When questioned by police this summer, Casey Anthony gave conflicting statements, including some that were later disproved, according to hundreds of documents and investigative reports released in the case.

She claimed she dropped Caylee off with a babysitter, but when police checked out her story, they learned the address Casey Anthony supplied belonged to an apartment that had been vacant for weeks. The woman Casey Anthony named as her babysitter told police she did not know her. Review a timeline of the case »

Investigators said cadaver dogs picked up the scent of death in Anthony's car as well as in her parents' backyard. They also said air quality tests conducted by the FBI found evidence consistent with human decomposition and chloroform in the car's trunk. A neighbor told police Anthony had asked to borrow a shovel.