Turkey, serving as the West's traditional window to Asia, the Middle East and multiple post-Soviet states, is a geographically strategic ally that's home to two U.S. Air Force bases. Brunson was moved after two years in prison, and placed under house arrest. He is on trial for terrorism charges.
Trump said Brunson "is suffering greatly".
Earlier, U.S. Vice President Mike Pence in a tweet threatened to impose "significant sanctions on Turkey until this innocent man of faith is free". The top USA diplomatic in Turkey, Philip Kosnett, released a statement saying he also visited the pastor and his wife, Norine.
Turkey on Friday hosted an American delegation for talks to address concerns about the potential negative impact on its economy of the looming reimposition of U.S. sanctions against Iran.
Brunson's case has been adjourned until October 12.
Trump said on Twitter last week that the pastor's detention was "a total disgrace". Otherwise, Congress wants the administration to block financing for Turkey's troubled economy from global lending institutions such as the International Monetary Fund and the World Bank. Turkey, however, has a different description for Andrew Brunson: They say he's a spy and an abettor of terrorists who is working to overthrow the government.
Turkey's lira currency briefly weakened to 4.89 to the dollar following reports of Pence's comments, but recovered later somewhat.
Trump's threat comes as the Turkish lira has lost one-fifth of its value this year over concerns about the central bank's ability to rein in double-digit inflation. Turkey has shown the political will to improve relations with the United States, he said, calling on Washington to engage in dialogue. "Erdogan has taken command over the economy and he has negative macroeconomic credibility, so we expect a serious current account crisis".
Aksoy called on the U.S.
A Turkish court ruled on Wednesday that an American pastor be transferred from jail to house arrest, his lawyer said, after almost two years in detention on terrorism charges in a case which has strained ties between Ankara and Washington.
Mr Brunson has denied charges of espionage, but faces up to 35 years in jail if found guilty.
Brunson is accused of ties to the movement of Fethullah Gulen, an Islamic cleric who lives in exile in the USA and whom Ankara blames for the coup attempt. Gulen denies any involvement in the coup, in which at least 250 people were killed.
Brunson's detention has deepened a rift between Washington and Ankara, which are also at odds over the Syrian war and Turkey's plan to buy missile defenses from Russian Federation.
On Wednesday, the Izmir 2nd High Criminal Court made a decision to turn Brunson's detention into house arrest due to his "health problems".
Pence said only that Turkish President Recep Tayyip Erdogan should be "prepared to face the consequences" if the pastor is not released immediately.
During the third and final day of the first-ever State Department ministerial to advance religious freedom, Pence and Pompeo also highlighted the plight of religious minorities across the globe.