The US state of Ohio has executed its first death row inmate in three years, ending a stoppage brought about by a legal dispute that followed an unusually drawn-out lethal injection in 2014.

Ronald Phillips, 43, who was convicted of raping and killing a three-year-old child, was put to death at the Southern Ohio Correctional Facility in Lucasville this morning, the Ohio Department of Rehabilitation and Correction said in a statement.

The execution had been delayed multiple times as a court dispute plays out over the state's use of a drug mixture for lethal injections. The US Supreme Court had denied appeals from Phillips last night.

Ohio's last execution took place in January 2014, when it became the first state to use a combination of the sedative midazolam and painkiller hydromorphone to execute Dennis McGuire.

McGuire's execution took 25 minutes and witnesses said he gasped and convulsed for 15 minutes.

Ohio implemented a moratorium in 2015 due to difficulty in obtaining lethal injection drugs. The following year the state said it would restart executions using a new drug protocol.

A federal court ruled in January that Ohio's new lethal injection process was problematic, delaying executions.

A three-judge panel from the sixth US Circuit Court of Appeals upheld the injunction in April, but that ruling was overturned in June by the full court.

Phillips' execution is the second scheduled for this week in the US.

Texas plans to execute Tai Chin Preyor, 46, tomorrow for killing a woman in a 2004 home robbery near San Antonio.

There have now been 15 executions in the US this year.