SAN DIEGO -- The grandmother of little Jahi Turner issued an emotional plea for the 2-year-old's return, and police said a search at a landfill for clues that may lead them to the boy could end as early as today.

MISSING JAHI TURNER Light-skinned African-American 30 pounds, 30 inches tall Black hair Wearing blue "Winnie the Pooh" T-shirt, blue pants, and gray tennis shoes INFORMATION SDPD Juvenile Hotline: (619) 744-9521 Tip Hotline: (619) 235-8477 Download A Missing Flyer SOUND OFF Share Your Thoughts

Jahi's maternal grandmother, Penny Thompson, arrived in San Diego four days ago from her Maryland home to assist in the search for the toddler.

"I am appealing ... for the return of my grandson," Thompson said at an impromptu news conference Sunday, her first public remarks since her arrival.

Thompson said that the investigation into Jahi's disappearance should be centered on finding the boy and not allegations cited in the news media, according to 10News.

"I want to keep the focus on Jahi, he is what is important. After we find him, if evidence comes out about how he came to be missing, then I'll deal with the madness," Thompson said, adding "I'm not here to blame anyone."

Police have declined to comment on news reports that Jahi was not where his stepfather, Tieray Jones, said he was on April 25, the afternoon the boy was reported missing, or that Jones failed a lie detector test.

The San Diego Union-Tribune reported that police did not find the boy's fingerprints on recreation equipment in the playground off 28th and Beech streets, where Jones said they had been that day.

Jahi's biological father, Tramane Sampson, arrived in San Diego Saturday from Maryland, as police and Marines continued to comb through a 5,000-ton mountain of garbage from Jahi's neighborhood dumped at a local landfill.

Police have declined to say what they are searching for in the Miramar landfill.

San Diego police information officer Dave Cohen told reporters on Friday that the search efforts at the landfill could be completed "as early as" today.

Crews have sifted through 80 percent of the garbage from the Golden Hill area, 10News reported.

Tieray Jones, 23, told police he left Jahi in Balboa Park with a woman and two other children for about 15 minutes while he went to a soda machine a few hundred yards away. When he returned, Jones said, Jahi and the others were gone.

Jahi's mother, Tameka Jones, is in the Navy and was at sea when her son disappeared. She immediately returned to San Diego.

Police have said that Tieray Jones is not a suspect in the case, 10News reported.

Jahi is black, light-skinned, about 30 inches tall and weighs 30 pounds. He was last seen wearing a blue, long-sleeve T-shirt with a "Winnie the Pooh" character on it, blue nylon pants with an orange drawstring and gray tennis shoes.

Police urged anyone with more information concerning Jahi's whereabouts to call the SDPD's Central Division "juvenile hotline" at (619) 744-9521, or San Diego County Crime Stoppers' anonymous tip service at (619) 235-8477.