Brunson, a 50-year-old North Carolina pastor who led a Protestant church in the city of Izmir along the Aegean coast, was one of 20 Americans arrested after the failed 2016 coup against Erdogan.
Turkish President Recep Tayyip Erdogan has long cited a separation of powers to say that he has no control over his country's judiciary, although in the past he has expressed an interest in trading "pastors" with the United States. He is facing up to 35 years in prison if found guilty of supporting the coup.
White House Press Secretary Sarah Huckabee Sanders told reporters Wednesday that the U.S.is imposing sanctions against Turkey due to the continued imprisonment of USA pastor Andrew Brunson. The United States has blamed both for being involved in Brunson's arrest and detention.
Mr Brunson is accused of aiding plotters of an attempted coup in 2016.
The Treasury Department's sanctions target Turkey's Minister of Justice Abdulhamit Gul and Minister of Interior Suleyman Soylu. The sanctions effectively block any property or interest in property controlled by them in the USA, and bar Americans from engaging in transactions with them.
Treasury accused the two of "implementing Turkey's serious human rights abuses".
TRT World was joined by Jon Brain in Washington DC and Andrew Hopkins in Ankara for the latest.
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"Give him [Gulen] to us, and we will try [Brunson] and give him back", Erdogan said in September.
Turkey's foreign ministry did not waste time in hitting back, saying: "There is no doubt that this will greatly damage constructive efforts working to solve the issues between the two countries".
US State Department spokeswoman Heather Nauert has also called the detention "unjust", adding, "Turkey knows our position well".
US officials have repeatedly said that Brunson is innocent and demanded his release.
"President Trump concluded that these sanctions are the appropriate action", Pompeo said.
One proposed bill would restrict loans from worldwide financial institutions to Turkey until Ankara stops the "arbitrary arrest and detention" of US citizens and consular staff. Language that calls for the release of Brunson and others has also been included in a defense authorization bill. The pastor has lived in Turkey for more than 20 years.
Last week, Ankara rebuked Trump's threats, which had been echoed by his Vice President Mike Pence.