The execution of a Tennessee death row inmate has been postponed after staff were unable to find a vein to administer a lethal drug.

Tony Carruthers, convicted of kidnapping and murdering three people in 1994, was set to be executed on Thursday.

But the state's Department of Corrections said that while its medical team did find a primary IV line to carry out the lethal injection, they could not find a suitable second vein to establish a backup line, which is required under lethal injection execution protocol.

In response, Tennessee Governor Bill Lee said he would grant Carruthers a temporary reprieve from execution for one year.

After finding the primary injection line, "the team continued to follow the protocol, but could not find another suitable vein", the corrections department said in a statement.

"The team attempted to insert a central line pursuant to the protocol, but the procedure was unsuccessful," the statement continued. "The execution was then called off."

Carruthers was convicted in 1996 for the kid­nap­ping and mur­ders of Marcellos Anderson, his mother Delois Anderson, and Frederick Tucker.

The men were beaten and shot and the three were buried alive in a Memphis cemetery.

Carruthers' case has drawn national attention as advocates like the American Civil Liberties Union (ACLU) have argued there were significant problems with his trial, including that he was forced to represent himself.

Carruthers himself has consistently maintained his innocence.

"His trial was riddled with errors. He was denied legal counsel. There was no physical evidence linked to him," the ACLU said in a press release demanding the "wrongful execution" of Carruthers be called off.

"The evidence against him that was presented at trial came from informants who have since recanted their statements or been discredited," the ACLU continued.

The nonprofit group also collected more than 130,000 signatures calling for the execution to be halted to allow for "necessary fingerprint and DNA testing".

Advocates and community groups delivered that petition to the governor's office at the Tennessee capitol on Monday, but Gov Lee announced the following day that Carruthers' execution would go forward as planned.

Last week, Kim Kardashian took up Carruthers' cause, urging her fans in a social media post to call the governor's office and demand the DNA evidence be tested "before it's too late", according to US media.

In a petition for clemency filed on Wednesday, attorneys for Carruthers argued that his current mental state - resulting from Schizoaffective Disorder, Bipolar Type, and brain damage - is too impaired for him to be executed.

"These disorders manifest in current symptoms of unending, synergistic, and complex delusions that thwart a rational understanding of his imminent execution," his lawyers argued.

In response to the news of the temporary reprieve, Maria DeLiberato, senior counsel at the ACLU's Capital Punishment Project, said the ACLU will continue fighting on Carruthers' behalf.

"Tennessee cannot continue torturing a man while refusing to answer serious questions about his innocence," DeLiberato said.