A woman in the US state of Georgia has been executed despite a number of last-ditch appeals, including one by the Pope, to try and block her execution.

Kelly Gissendaner, 47, was the first woman put to death in the southern US state in 70 years.

Lawyers filed at least three appeals with the US Supreme Court to try and delay the sentence hours before she died, but all failed.

Gissendaner planned her husband's murder in 1997.

Her former lover, who killed her husband, was given life in prison.

Pope Francis, who was recently on a US tour, urged the review board to reconsider. But on Tuesday afternoon, the board announced it was not granting clemency.

And hours later, the US Supreme Court said it had rejected three applications for a stay of execution.

Protesters had been calling on the board to spare her life. Photo: AP

Witnesses to the execution told a local Fox News affiliate she was singing Amazing Grace before she was given a lethal injection.

The Pope's appeal for Gissendaner's life was made in a letter written by his diplomatic representative in the US, Archbishop Carlo Maria Vigano, on Tuesday.

The archbishop wrote that, while not wishing to minimise the gravity of the crime, he implored the board "to commute the sentence to one that would better express both justice and mercy".

The board also heard evidence from Gissendaner's lawyers who said she had undergone a transformation in prison, offering support to troubled inmates and showing remorse for her own crime.

Former Georgia Supreme Court Chief Justice Norman Flether also made representations to say Gissendaner's death sentence was disproportionate to the crime that she committed.

She was convicted of murder in relation to the 1997 stabbing death of her then-husband, Douglas Gissendaner.

Gissendaner was the only woman on Georgia's death row. Photo: AP

She did not actually kill him, but rather encouraged her lover, Gregory Owen, to commit the act.

Owen later took a plea deal and testified against Gissendaner, and for his co-operation was sentenced to life in prison. He will become eligible for parole in 2022.

Douglas Gissendaner's family said in a statement on Monday that Kelly Gissendaner's sentence was appropriate.

"She had no mercy, gave him no rights, no choices, nor the opportunity to live his life," the family said.

Gissendaner has had two previous execution dates.

Officials were unable to carry out her sentence in February due to inclement weather, and the next date in March was cancelled after officials said the drug used in the lethal injection was cloudy.