A Missouri man convicted of killing his live-in girlfriend and her three young children has been executed despite his claims he was in another US state when the killings took place.

Raheem Taylor, 58, is the third Missouri inmate put to death since November at the state prison in Bonne Terre.

It was the nation’s fifth execution this year, following a previous execution in Missouri, two in Texas and one in Oklahoma. All were by lethal injection.

Taylor kicked his feet as pentobarbital was administered, then took five or six deep breaths before all movement stopped.

In a final statement, Taylor said Muslims do not die but “live eternally in the hearts of our family and friends”.

“Death is not your enemy, it is your destiny. Look forward to meeting it. Peace!” he wrote.

Taylor, who previously went by the first name Leonard, long maintained he was in California when Angela Rowe, her 10-year-old daughter Alexus Conley, six-year-old daughter AcQreya Conley and five-year-old son Tyrese Conley were killed in 2004.

His supporters included the national NAACP, nearly three dozen civil rights and religious groups and the Midwest Innocence Project.

But Taylor’s innocence claims were turned aside time and again.

St Louis County’s prosecuting attorney Wesley Bell, a Democrat, last week declined Taylor’s request for a hearing before a judge, saying the “facts are not there to support a credible case of innocence”.

Republican governor Mike Parson declined to grant clemency on Monday, the same day the Missouri Supreme Court denied a stay request.

Earlier on Tuesday, the US Supreme Court declined to intervene.

Gerauan Rowe, Angela Rowe’s sister, said after the execution that moving on remains difficult, more than 18 years after she lost her sister, nieces and nephew.

“I’m at a point in my life right now — I’m OK but I’m not,” she said. “But I know justice was served. It’s kind of hard trying to move forward but I think I can do it.”

There was no question that Taylor was not in Missouri when the bodies were found. But what is not known for sure is when the family was killed.

Taylor and Angela Rowe lived with the children at a home in the St Louis suburb of Jennings. Taylor boarded a flight to California on November 26 2004.

On December 3 2004, police were called to the home in Jennings after worried relatives said they had not heard from Ms Rowe. Officers found the bodies of Ms Rowe and her children. All four had been shot.

A pathologist’s initial finding was that the killings likely happened within a few days before the bodies were discovered – when Taylor was in California.

But at Taylor’s trial, pathologist Phillip Burch said the murders could have happened two or three weeks before the bodies were found.

Taylor’s lawyer, Kent Gipson, said several people, including relatives of Ms Rowe and a neighbour, saw Ms Rowe alive in the days after Taylor left St Louis.

Meanwhile, Taylor’s daughter in California, Deja Taylor, said in a court filing she and her father called Ms Rowe and one of the children during his visit.

Deja Taylor’s mother and sister corroborated her story, the court filing said.

Bob McCulloch, who was St Louis County’s elected prosecutor at the time of the killings, said Taylor’s claim of innocence was “nonsense” and the alibis provided by his daughter and her relatives were “completely made up”.

Mr McCulloch told the Associated Press that evidence suggested Ms Rowe and the children were murdered on the night of November 22 or 23, at a time when Taylor was still in St Louis.

He said Ms Rowe typically made about 70 outgoing calls or texts each day. From November 23, she made none.

Meanwhile, DNA from Ms Rowe’s blood was found on Taylor’s glasses when he was arrested, a relative taking him to the airport saw Taylor throw a gun into the sewer and Taylor’s brother told police Taylor admitted to the crime, Mr McCulloch said.

Authorities believe Taylor shot Ms Rowe during a violent row, then killed the children because they were witnesses.

All three recent Missouri executions involved cases from St Louis County.

Kevin Johnson was executed in November for killing a police officer in 2005 and Amber McLaughlin was put to death on January 3 for killing a woman in 2003.

McLaughlin’s death is believed to be the first execution of a transgender woman in the US.