"At the president's direction, the Department of the Treasury is sanctioning Turkey's minister of justice and minister of interior, both of whom played leading roles in the arrest and detention of Pastor 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.
Brunson, who has lived in Turkey for almost two decades, was arrested later that year and charged with complicity in the attempt to overthrow Erdogan's government.
Brunson was held for almost two years in prison on terror-related charges before he was moved last week to house arrest.
Vice President Mike Pence, who like Brunson is an evangelical Christian, has declared him "a victim of religious persecution".
"The aggressive attitude of the US serves no objective", it said in a statement, adding that Turkey would reciprocate "without delay".
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Nevertheless, Turkish President Recep Tayyip Erdogan said the USA "cannot make Turkey back down with sanctions", and warned the US risks losing "a strong and honest partner like Turkey".
Turkish Foreign Ministry on Wednesday strongly protested against U.S. Treasury Department's decision, calling on the U.S. administration to reverse its "wrong decision".
"If Turkey does not take immediate action to free this innocent man of faith and send him home to America, the United States will impose significant sanctions on Turkey until Pastor Andrew Brunson is free", the vice president said.
In a statement issued as he was en route to meetings in East Asia, Secretary of State Mike Pompeo said that the "Turkish government refused to release Pastor Brunson after numerous conversations between President Trump and President Erdogan, and my conversations with Foreign Minister Cavusoglu".
A Turkish minister has defiantly mocked US sanctions against him, saying his only asset in the United States is a USA -based Muslim cleric whom Turkey blames for a failed coup and wants extradited.
"President Trump concluded that these sanctions are the appropriate action", he said.
"We are still pursuing a diplomatic approach", Nauert said.
US President Donald Trump and Turkish counterpart Recep Tayyip Erdogan met during a North Atlantic Treaty Organisation summit in July.