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A Turkish court rejected an appeal to release from house arrest a US pastor whose detention on terror-related charges has strained relations between NATO allies Ankara and Washington, state media reported on Tuesday.

The court in the Aegean region of Izmir rejected an appeal by the lawyer for Andrew Brunson, who ran a Protestant church, to have him released from house arrest and have his travel ban removed, state-run Anadolu news agency said.

Last week, the court ordered that Brunson, who had spent almost two years in jail after his initial detention in October 2016, be moved from jail to house arrest at his home in Izmir.

But the move stoked tensions rather than defusing the crisis, with US media reports accusing Turkey of reneging on a deal to free him, which Ankara has denied.

US President Donald Trump threatened to impose "large sanctions" on Turkey if the pastor was not freed, following similar warnings from his Vice President Mike Pence.

But Turkish President Recep Tayyip Erdogan insisted that sanction threats would not force Ankara to take a "step back", in comments reported on Sunday.

Relations between Turkey and the United States have been tense over multiple issues including American support for a Syrian Kurdish militia who Turkey claims are terrorists, as well as the failure to extradite US-based Muslim preacher Fethullah Gulen.

Ankara accuses Gulen of organising the July 2016 failed coup, claims which he denies.

Brunson risks up to 35 years in jail if convicted of carrying out activities on behalf of two organisations Turkey deems to be terror groups: the Gulen movement and the Kurdistan Workers' Party (PKK).

Brunson denies the charges while US officials have repeatedly stressed that Brunson is innocent. Trump has previously called the pastor a "fine gentleman".

Brunson is one of several American nationals caught up in the crackdown after the attempted putsch two years ago.

NASA scientist Serkan Golge, a dual national, was jailed for seven-and-a-half years in February for being a member of Gulen's movement. Two employees from American missions in Turkey remain in custody and another under house arrest.

The next hearing in Brunson's trial is on October 12.

Turkish Foreign Minister Mevlut Cavusoglu is expected to meet US Secretary of State Mike Pompeo during this week's meeting of the Association of Southeast Asian Nations (ASEAN).