Marvallous Keene, 36, who was convicted in five of the murders, chose not to file a late appeal over his death sentence.
He died by lethal injection at the Southern Ohio Correctional Facility in Lucasville - seven days after Ohio's last execution. It was the fastest turnaround since the state executed two inmates in six days in 2004.
The European Union presidency, currently held by Sweden, released a statement noting the 1,000th lethal injection execution and calling on the US to halt executions, pending the abolition of the death penalty.
"The European Union is opposed to the use of capital punishment in all cases and under all circumstances," the statement said. "We believe that the abolition of the death penalty is essential to protect human dignity, and to the progressive development of human rights."
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The death penalty is abolished in the European Union, and the United Nations General Assembly has called upon all countries that use it to stop executions and end the practice.
The Ohio Supreme Court, in denying a request last month to delay Keene's execution, said it would schedule future executions at last three weeks apart so that public defenders will have more time to prepare clemency cases for inmates who wish to pursue it.
Ohio has one execution scheduled per month through February 2010.