(CNN) -- A death row inmate who says he did not commit the murders he was convicted of asked the Arkansas Supreme Court on Thursday to grant him a new trial.

Damien Echols maintains his innocence 16 years after he and two other teens were convicted of murdering

three Cub Scouts -- Michael Moore, Christopher Byers and Steven Branch.

The court, which heard his request for a new trial Thursday morning, is likely to rule in two or three weeks, court representative Stephanie Harris said.

Echols spoke to CNN from death row recently about the new evidence that he says will prove his innocence.

"I miss the things that most people take for granted, things people don't want, like rain," Echols told CNN in a face-to-face interview.

"To go out and touch it and get wet, or to feel snow. I loved snow my entire life, and I haven't had that in almost 20 years now."

On May 6, 1993, police in the rural community of West Memphis, Arkansas, found the bodies of the young boys, bruised and mutilated, their arms and legs hogtied with their own shoelaces.

Echols, along with 16-year-old Jason Baldwin and 17-year-old Jessie Misskelley, were found guilty a year later. Echols received a death sentence, while Baldwin and Misskelley were sentenced to life in prison. The three teens became known as the West Memphis 3.

His lawyers want to present DNA evidence not available at the time of the trial, as well as testimony that supports arguments that Echols and the two others did not commit the crime.

Meanwhile, no execution date is set for Echols.

"We are asking the Arkansas Supreme Court to right a terrible wrong, overturn their convictions and grant Damien as well as Jason Baldwin and Jessie Misskelley a new trial," said Dennis Riordan, the lead attorney on the case.

The West Memphis 3 have gained advocates, including unexpected support from some of the parents of the victims. Last year, Pamela Hobbs, mother of victim Steven Branch, told CNN that she was once convinced of their guilt. Then she began to consider the DNA evidence. She now says she believes the prosecution's case was flawed.

Capi Peck formed Arkansas Take Action, a Little Rock-based group trying to raise awareness about the West Memphis 3. In the past few weeks, the group has brought in celebrities such as Eddie Vedder of the rock group Pearl Jam and actor Johnny Depp to a public rally.

Echols says police questioned him a day after the bodies of the second-graders were found in the woods, near where they used to hunt turtles. A month later, the teens were arrested.

Prosecutors successfully argued the defendants were involved in a satanic cult. They said that punctures and cuts on the boys' bodies indicated a ritual sacrifice.

In addition, prosecutors secured a confession from Misskelley, although his defense attorneys argued that he had a learning disability and an IQ of 70.

They also claimed that it was not only riddled with inconsistencies but was coerced.

Neither his parents nor his attorney was present when he was questioned. His confession came during the last hour of a 12-hour police interrogation.

His attorneys tried to convince the Arkansas Supreme Court that new evidence not available during the trial exonerates Echols.

DNA testing indicated that a hair found on the shoelace used to tie up one of the victims is consistent with a hair from Terry Hobbs, the stepfather of victim Steven Branch, Echols' lawyers said.

Police have never considered Hobbs a suspect and Hobbs maintains that he had nothing to do with the murders.

Asked whether he killed the boys, Echols responded, "To constantly have to answer that question and to constantly have people asking you that question is like being kicked in the stomach over and over again."

CNN's Deborah Feyerick and Stephanie Chen contributed to this report.