The case of Andrew Brunson, an evangelical Christian, is one of a series of disputes that lies at the heart of deteriorating ties between the two North Atlantic Treaty Organisation allies.
The embattled Turkish lira tumbled more than 16% to new record lows against the dollar as strains with the USA intensified over Brunson, as well as Washington's co-operation with the Syrian Kurdish militia force in the fight against Islamic State and other forces in Syria.
All eyes will be on the lira when foreign exchange markets reopen on Monday after the weekend break.
No body, no state and no credit rating agency can threaten Turkey and Turkish people, he added.
"Interest rates should be kept to a minumum because they are a tool of exploitation that makes the poor poorer and the rich richer", Erdogan said in a speech in the Black Sea city of Rize.
"We've stood with neighbours before, and will again now".
Turkey and the U.S. have disagreed on a number of issues since Trump came into office, including Washington's support of Kurdish groups in neighbouring Syria and its refusal to extradite Fethullah Gülen, the cleric Erdogan claims is behind the botched attempt to unseat him.
Erdogan noted that his country would turn to other partners if this "economic war" goes on.
"Hopefully we will overcome this disaster and we will also successfully overcome this economic war", Erdogan said.
"During this period, Turkey has set records in its exports, production and employment", Erdogan said.More news: José Mourinho explains choice to make Paul Pogba captain vs. Leicester
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He further added that the only response to a country which chooses to sacrifices its strategic partnership and a half century alliance with a state with a population 81 million for the sake "terror groups" is "good-bye".
American pastor Andrew Brunson has been held since October 2016 on charges of terror and espionage, and if convicted, could face a jail term of 35 years. Mr Trump has described his detention as a "total disgrace" and urged Erdogan to free him immediately.
A Turkish delegation visited Washington for talks this week but left with no signs of a breakthrough.
The two North Atlantic Treaty Organisation members are at odds on a number of issues - how to fight the Islamic State group, Ankara's plans to buy Russian missile defence systems, and how to punish the alleged plotters of a failed coup in Turkey in 2016.
Erdogan mentioned the deadline in comments he made Sunday to his supporters in Trabzon, according to Reuters.
The currency's drop - 41 percent so far this year - is a gauge of fear over a country coming to terms with years of high debt, worldwide concern over Erdogan's push to amass power, and a souring in relations with allies like the U.S.
The lira's crash was sparked by a disagreement with the United States over the detention of an American pastor in Turkey, which has even brought up questions over the future partnership between Washington and Ankara.
The central bank has over the last weeks defied calls from markets for rate hikes to combat these problems, raising fears of interference from Erdogan who has repeatedly called for low interest rates.
Since the assassination of the United States pastor Andrew Branson in Turkey and the introduction of sanctions the relations between the two North Atlantic Treaty Organisation allies have fallen to their lowest levels in the last few decades.
Mr. Erdogan repeated his call for Turks to sell dollars and buy lira to shore up the currency, while telling business owners not to stock up on dollars.