A 50-year-old man convicted of murdering his estranged wife and sexually assaulting his step-daughter was executed on Wednesday in the southern US state of Mississippi, local media said.

David Cox, a former truck driver, was put to death by lethal injection at the Mississippi State Penitentiary in Parchman.

"I want my children to know that I love them very much and that I was a good man at one time," Cox said in his last words, according to state department of corrections commissioner Burl Cain, the Clarion Ledger newspaper reported.

"Don't ever read anything but the King James bible. I want to thank the commissioner for being so very kind to me. And that's all I got to say," Cox reportedly said.

In 2009, Cox's wife Kim Cox told police that Cox had sexually assaulted her daughter from a previous relationship.

Cox spent nine months in prison before being released on bond.

After his release, he bought a handgun and broke into a home where Kim Cox was staying with their two young sons and her daughter.

After shooting his estranged wife, Cox sexually assaulted his then 12-year-old step-daughter in front of her dying mother.

Cox was sentenced to death in 2012 after pleading guilty to murder, sexual assault and other charges.

Three years ago, Cox began writing to the courts to ask that his lawyers, who were seeking to halt his execution, be fired and that his execution be allowed to go ahead.

In one letter, he described himself as a "guilty man worthy of death."

In another, he asked a judge to set a date to "execute my body for crimes of in which I did committ (sic) in premeditation, anger and joy."

The Mississippi Supreme Court agreed with evaluations that Cox was mentally competent and a date was set for his execution.

Kim Cox's daughter told the Daily Journal newspaper that she intended to attend the execution.

Cox was the 10th person executed in the United States this year and the first since 2012 in Mississippi.

The state has faced difficulties for several years in obtaining the drugs used to carry out executions by lethal injection.

Many pharmaceutical laboratories refuse to sell the products to US states that intend to use them for capital punishment.