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US President Donald Trump kicked off a campaign rally in Richmond, Kentucky, by celebrating the release of American pastor Andrew Brunson and thanking Turkish President Recep Tayyip Erdogan for his cooperation.

Trump said the pastor's release could mark the start of a "terrific relationship" between Washington and Ankara.

"I want to thank President Erdogan of Turkey - he was terrific. We all worked together, it wasn't easy... we don't pay ransom. I want to thank the people of Turkey and I think we'll probably now really establish a terrific relationship with Turkey," he said.

Brunson was hosted at the Oval Office on Saturday after spending two years of confinement in Turkey.

A Turkish court in the western port city of Aliaga convicted Brunson on charges of espionage and aiding terror groups.

He was sentenced to one month and 15 days in jail until a court reduced his sentence on Friday and released him based on time served and good behaviour.

Following accusations that the state had directly intefered in the judiciary over the case, Erdogan said the court's decision was "taken independently".

Both Trump and Erdogan have denied reports of a secret deal to secure the 50-year-old Brunson's release.

The US and Turkey are at the centre of a new crisis with Saudi Arabia, after American resident and journalist Jamal Khashoggi went missing during a visit to the Saudi embassy in Istanbul last week.

Turkish investigators believe he was murdered by Saudi agents on the consulate's grounds and Trump has vowed "consequences" if Saudi Arabia is found to be behind the journalist's killing.