Andrew Craig Brunson, an evangelical pastor from North Carolina, arrives at his house in Izmir, Turkey. Brunson, who had been jailed in Turkey for more than one and a half years on terror and espionage charges, was released Wednesday and will be put under house arrest as his trial continues. Picture: Emre Tazegul/AP

Washington - The United States "will impose large sanctions" on Turkey over the continued detainment of pastor Andrew Brunson, US President Donald Trump warned on Thursday, calling him a "great Christian."

The threat marked a significant escalation in already tense relations between the two NATO allies over a range of issues - from Syria to Turkey's purchasing of advanced Russian air defence systems - that have seen the governments grow further apart.

The president's remarks on Twitter came shortly after a tough speech by Vice President Mike Pence in which he warned sanctions would come if Turkey did not take "immediate action" to release the pastor, who was arrested in 2016.

Turkey's Foreign Minister responded by saying that Turkey was governed by the rule of law. "We will never tolerate threats from anybody," Mevlut Cavusoglu said on Twitter.

"No one can threaten or give orders to Turkey," said Hami Aksoy, a spokesman for the ministry. Turkey has shown the political will to improve relations with the US, he said, calling on Washington to engage in dialogue.

"Release pastor Andrew Brunson now or be prepared to face the consequences," Pence said, addressing Turkish President Recep Tayyip Erdogan and the Turkish government directly, calling the detainee "an innocent man - there is no credible evidence against him."

Pence spoke by phone this week with Brunson and is in contact with his family. The top US diplomatic in Turkey, Philip Kosnett, released a statement saying he also visited the pastor and his wife, Norine.

"We will continue working until Andrew Brunson is a free man and there is justice for him and for other unjustly detained American citizens and local Turkish employees of the US diplomatic mission," Kosnett said, referring to additional concerns of Washington.

The arrest of the local staff caused a serious rift last year, with both countries temporarily suspending visa services for one another's citizens for nearly three months.

Trump used his Twitter account to back up the speech by his deputy about the 50-year-old pastor, originally from the state of North Carolina, who has lived in Turkey for two decades, preaching at a small congregation in Izmir, on the Aegean coast.

"The United States will impose large sanctions on Turkey for their long time detainment of Pastor Andrew Brunson, a great Christian, family man and wonderful human being," Trump wrote. "He is suffering greatly. This innocent man of faith should be released immediately!"

Brunson - indicted in Turkey on terrorism charges - was moved to house arrest this week after spending about a year-and-a-half behind bars. Pence said Thursday that this was a welcome first step but "not good enough."

The vice president noted that tens of thousands of people have been arrested in Turkey since a failed military coup attempt in July 2016, including journalists, activists, judges, teachers and military officers.

Against expectations, a court in Izmir on July 19 denied a request to release Brunson, sparking Trump to term the pastor a "hostage."

Brunson is accused of ties to the movement of Fethullah Gulen, an Islamic cleric who lives in exile in the US and whom Ankara blames for the coup attempt. Brunson is also accused of links to the banned Kurdistan Workers' Party (PKK), a secular-leftist militia.

Erdogan suggested last year that Brunson's case could be connected to an extradition request for Gulen, who lives in Pennsylvania.

Anger over Turkey in the US has branched across partisan lines, with lawmakers on the left and right increasingly critical of Ankara and seeking to impose sanctions, which could include being left out of the F-35 military plane program.

There are also lingering issues over a Turkish state-run bank that was allegedly involved in busting sanctions on Iran, which hangs in the background as Trump looks to impose a fresh sanctions regime on Iran.

Turkey relies on Iranian energy and has indicated it will not acquiescence to US demands to cut off supplies from its neighbour, potentially posing further risks.

The rising acrimony comes just months ahead of US midterm elections in November, with Trump's conservative Republican Party seeking to hold its majority in both houses of Congress.