American officials have also protested the detentions of several Turkish employees of the US diplomatic mission in Turkey, including Metin Topuz, Hamza Ulucay and Mete Canturk.
Brunson is charged with spying for the PKK - a designated terrorist group in the U.S. and Turkey - and the Fetullah Terrorist Organization (FETO), the group behind the defeated July 2016 coup attempt in Turkey during which 251 people died and thousands were injured. Brunson runs an evangelical church in the Turkish city of Izmir.
Brunson is being tried on espionage and terrorism-related charges that he rejects.
He faces up to 35 years in prison.
Deepening a spat that has rattled financial markets and threated to split a long-standing defense and political alliance, Treasury Secretary Steven Mnuchin suggested the next spiral of tit-for-tat sanctions was coming soon.
Turkey retaliated with 533 million dollars (£419 million) of tariffs on some U.S. imports - including cars, tobacco and alcoholic drinks - and said it would boycott USA electronic goods.
Donald Trump stumps in central OH for 12th congressional candidate
In calling three prominent African-Americans all but stupid, Trump once again left himself open to accusations of racism. The crowd cheered and chanted the campaign staple rallying cry, "Build the wall, build the wall".
The prospect of the United States and China returning to the table instead of trading tariff increases brought some relief to investors. "It did not. The United States reaction was far from satisfactory".
Turkey is calling for the U.S.to extradite a Pennsylvania-based Muslim cleric accused engineering a 2016 coup attempt.
That had knocked other Asian tech firms with South Korea's Samsung Electronics, Asia's third-largest firm by market cap, down to a one-year low. Erdogan previously suggested a swap in which Brunson is released in exchange for Gulen, though USA officials have said Turkey must present convincing evidence for any extradition proceeding to be considered. Last week, Erdogan wrote, "Washington must give up the misguided notion that our relationship can be asymmetrical and come to terms with the fact that Turkey has alternatives".
Turkish officials said Mr Erdogan spoke with French president Emmanuel Macron, during which the French president said Turkey's economic stability is important for France.
His efforts have also found some success in the Middle East.
Qatar said it would provide "a host of economic projects, investments and deposits" worth 15 billion dollars to support Turkey's economy.
The Chinese currency's slide in recent months, partly on the back of concerns about what a full-blown trade war with the US would do to China's economy, has rattled investors.
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