Florida has executed a schizophrenic man who believed that he was the immortal prince of God vested with superhuman powers including an ability to control the sun, despite the US constitution's prohibition against putting mentally ill people to death.

John Ferguson, 65, was killed by lethal injection at 6pm on Monday. Earlier in the evening the US supreme court declined to hear a final petition from his lawyers. Although there was overwhelming evidence that the court's own interpretation of the US constitution was being disregarded, the justices gave no explanation for their decision to remain on the sidelines and allow the killing to go ahead.

Ferguson's legal team, backed by a raft of prominent legal and mental health organisations, had appealed to the nation's highest legal panel to step in on grounds that the execution would be a flagrant violation of the Eighth Amendment of the US constitution that bars "cruel and unusual punishment".

Nobody disputes that Ferguson was guilty of a singularly gruesome sequence of murders. He was part of a group that killed six people in the course of an armed robbery in Carol City, in 1977, and then went on the following year to kill two 17-year-old school students, Belinda Worley and Brian Glenfeldt, in the same Florida area.

But opponents of the execution argue that he should have been transferred to a life sentence with no chance of parole – in other words, he would spend the rest of his natural life in jail – because he was mentally ill and had been consistently since well before he committed the crimes. A chart put together by his lawyers showed that he was first diagnosed as having visual hallucinations by a Florida state prison psychologist in 1965.

Before he had taken part in the mass murder, he had been diagnosed as a paranoid schizophrenic who demonstrated evidence of active psychosis. He was found in numerous medical examinations to be grossly psychotic, insane and incompetent.

In their petition to the US supreme court, filed last week, Ferguson's lawyer Ben Lewis chronicled the prisoner's persistent delusions. They included the belief that he could not be killed because he had powers drawn from the Sun, and a delusion that his prison guards were communists who were out to kill him because they knew that he was in fact the prince of God.

"John Ferguson is without a doubt mentally ill. He has a 40-year history of paranoid schizophrenia, we have more than 30 doctors diagnosing him as that over four decades. Yet Florida is close to eviscerating the US supreme court law that makes him ineligible for execution," Lewis told the Guardian.

Ferguson was convinced that his impending execution was a conspiracy against him to prevent him wielding his sun-given powers, rather than the retributive consequence of his criminal acts, and that his execution would be the completion of a plot by the state of Florida to prevent him ascending to his rightful throne at God's right hand.

In 2007, in the case of Panetti v Quarterman, the supreme court ruled that a prisoner about to be executed must not only be aware of the punishment they are about to receive, but also have a "rational understanding of it". Ferguson, who believed he was being put to death because he was the anointed prince of God, would appear not to have met this standard.

Yet the state supreme court of Florida found that he was eligible for the gurney, making the interesting argument that Ferguson's belief in his own immortality was shared by millions of other American Christians. The federal appeals court for the 11th circuit concurred with the Florida courts and allowed the execution to proceed, even though one of the federal judges dissented that the application of the law in this case had been "patently wrong".

The execution of a mentally ill man in violation of the US constitution has echoes with the recent case of Warren Hill, who came close to execution in Georgia last month despite the constitutional prohibition of the death penalty for people with intellectual disabilities. As the New York Times has put it in an editorial: "even where standards are clear, some states seem untroubled by carrying out a death sentence that violates the Constitution."