A higher court in Izmir upheld a lower-court decision that rejected the lifting of Brunson's house arrest, according to the state-run Anadolu agency and the newspaper HaberTurk.
The Committee of Concerned Scientists has compared the Brunson case to that of Serkan Golge, a NASA scientist who was arrested at the time of the coup attempt and was sentenced to more than seven years in prison for alleged links to Gulen's group.
The lira, which has lost some 40 percent of its value this year, weakened beyond 6.21 against the U.S. dollar after the news, from 6.04 beforehand.
The man has been detained by Turkish authorities for almost two years.
Also Friday, in more verbal sparring, Turkey's trade minister said her government would respond in kind to any new trade duties from the United States after U.S. Treasury chief Steve Mnuchin said the U.S. could put more sanctions on Turkey if the pastor is not released soon.
"We have more that we are planning to do if they don't release him quickly", Mnuchin said.
Meanwhile, Mr Trump said that the United States "will pay nothing" to Turkey for the release of detained American pastor Andrew Brunson, who he called "a great patriot hostage".
Trump said the United States had helped Turkey in a related incident, but that the North Atlantic Treaty Organisation ally had not repaid the favour. Trump said on Twitter.More news: EPL: Mourinho tells Pogba to 'leave' Manchester United
"I call out to those in the United States". Referring to imprisoned pastor Andrew Brunson, Trump said "they have a great Christian pastor there, he's a very innocent man".
"They should have given him back a long time ago, and Turkey has in my opinion acted very, very badly, " Trump told reporters on Friday. He criticized Turkey for "holding our wonderful Christian Pastor". "He's an innocent man".
A Trump administration official told the Associated Press Thursday that National Security Adviser John Bolton spoke Monday with the Turkish ambassador to the USA telling him to release Brunson.
Turkey, in turn, criticized the prosecution in the USA of Mehmet Hakan Atilla, a top official at Turkey's state-controlled Halkbank who was convicted of helping Iran avoid US sanctions. Brunson is accused of being linked to Fethullah Gulen, a US-based cleric who Ankara has said was the mastermind behind the botched coup attempt in July 2016.
"They missed a big opportunity". He demanded Brunson's release, saying "they can't take our people".
The dispute over Mr Brunson and other frictions between Washington and Ankara have been one reason the Turkish lira has plunged 40 percent this year.
The lira lost strength after Mnuchin's remarks.
Last week, Trump tweeted that his administration was doubling aluminium and steel tariffs for Turkey, and in response Ankara sharply hiked tariffs on some United States products.