The US has threatened to impose more economic sanctions on Turkey if it does not free a detained American pastor.
Andrew Brunson has been held in Turkey for nearly two years over alleged links to political groups.
The dispute over his release has seen the two Nato allies impose tariffs on one another’s goods.
This has worsened a crisis for Turkey’s currency, the lira, which has lost about a third of its value against the dollar since January.
This has prompted widespread selling in other emerging markets, sparking fears of a global crisis.
The currency had recovered slightly earlier this week after the government increased tariffs on imports from the US of cars, alcoholic drinks and leaf tobacco.
But the recovery was overshadowed by the fresh threats from the US.
Last week, the US doubled its tariffs on metal imports from Turkey, and on Thursday, US Treasury Secretary Steven Mnuchin said: “We have more that we are planning to do if they don’t release him [Mr Brunson] quickly.”
Turkey is accusing Mr Brunson – who operates a small church in Izmir – of having links to the outlawed Kurdistan Workers Party and the Gulenist movement, which Turkey blames for a failed coup two years ago.
Mr Trump tweeted that Turkey had “taken advantage of the United States for many years” and that Mr Brunson was a “patriotic hostage”.
“We will pay nothing for the release of an innocent man, but we are cutting back on Turkey,” he said.
The influential Protestant evangelical church in the US is a major support base for Mr Trump.
The dispute with Turkey comes at a time when Mr Trump is fighting a trade war with China.
Turkey’s central bank said on Monday that banks would be given all the liquidity they needed, as it seeks to keep money flowing in the financial system.
There are signs that the weakness in Turkish currency markets is already spreading.
South Africa’s rand, Russia’s rouble, the Indian rupee and Indonesia’s rupiah have all taken a hit from the crisis in Turkey.