By Jeff Franks

HOUSTON (Reuters) - A group whose work in finding flawed convictions contributed to a death penalty moratorium in Illinois urged Texas Gov. George W. Bush on Monday to grant a reprieve to a man scheduled for execution in 10 days.

The Center for Wrongful Convictions at Northwestern University said Texas, which leads the nation in capital punishment, may kill an innocent man if Republican presidential hopeful Bush allows the June 22 execution of Gary Graham.

In a news conference, center legal director Lawrence Marshall said Graham, convicted in the 1981 robbery and shooting death of a man outside a Houston supermarket, was facing execution on "the weakest evidence I've seen in 30 years."

"Of the 684 men and women who have been executed in this country (since 1976) I am aware of none who was executed in the face of such overwhelming doubt of guilt," Marshall said.

In January, Illinois Gov. George Ryan, a Republican and capital punishment supporter, suspended executions in his state because of evidence that 13 men on death row had been wrongly convicted. In nine of those cases, the information was unearthed by students and professors at Northwestern.

Graham, now 38, was sentenced to die largely on the testimony of a single witness who picked him out of a police lineup.

Six other witnesses who have cast doubt on Graham's guilt either were not called to testify in his trial or have come forward since, Marshall said.

Graham has maintained his innocence in the crime, but pleaded guilty to 10 other aggravated robberies committed around the same time and is serving 20 years in prison.

Graham, whose case has attracted the support of celebrities such as actor Danny Glover, was granted a stay in 1993 by then Texas Gov. Ann Richards, a Democrat.

Bush spokesman Mike Jones said on Monday the governor would wait for the Texas Board of Pardons and Paroles recommendation on a clemency request from Graham before deciding what to do.

Bush, a death penalty supporter who became governor in January 1995, recommended his first stay of execution for a death row inmate two weeks ago in a case where the inmate said DNA tests could clear him in the rape and murder of his stepdaughter.

Texas, with 218 executions since a national death penalty ban was lifted in 1976, leads the nation in capital punishment. Under Bush, 131 people have been put to death by lethal injection, including 19 this year.