On Wednesday, the lira traded at 6.4125 to the United States dollar, weakening from a close of 6.3577 a day earlier.
The United States and Turkey have exchanged tit-for-tat tariffs in an escalating attempt by Mr Trump to induce Turkish president Tayyip Erdogan into giving up Mr Brunson, who denies charges that he was involved in a coup attempt against Mr Erdogan two years ago.
"Pastor Andrew Brunson is an innocent man held in Turkey & justice demands that he be released".
USA stocks and emerging market currencies rebounded on Thursday after China said it will hold trade talks with the United States later in August and Turkey's lira continued its recovery.
Turkey retaliated with some $533 million of tariffs on some USA imports - including cars, tobacco and alcoholic drinks - and said it would boycott US electronic goods, singling out Iphones.
Many countries had been the target of similar United States trade measures, Albayrak said on Thursday, and Turkey would navigate this period with other parties such as Germany, Russia and China.
On Wednesday, a court in Izmir, where Brunson is on trial, rejected his appeal to be released from house arrest.
iPhone owners in Turkey are smashing their mobile devices as a symbolic gesture of support for their government amid ongoing clashes and a strained relationship with the Trump administration.
In a tweet on Thursday, Trump urged Brunson to serve as a "great patriot hostage" while he is jailed and criticized Turkey for "holding our wonderful Christian Pastor".
"The tariffs that the United States placed on Turkey were out of national security interests, theirs are out of retaliation", she noted, refusing to reveal USA further actions to respond to Ankara's statement.
"We believe that the wave of RMB depreciation is probably over and that renewed fiscal stimulus (in China) will bring a halt to decelerating growth as well as higher interest rates supporting a stronger RMB", Alicia Garcia Herrero, chief economist for Asia Pacific at Natixis, said in a note.
Turkish officials say Brunson's case is a matter for the courts. Few saw a Bank of England interest rate hike earlier this month as a vote of confidence in the economy, since Britain's future, and access to European markets, remains in doubt. We are with Turkey.
Turkey was quick to broadcast a Qatari pledge to directly invest $15 billion into Turkey after Qatar's emir visited on August 15.
Sanders also criticized Turkey's imposition of tariffs on some USA goods as "regrettable and a step in the wrong direction".
JP Morgan said moves by Turkish authorities showed they were committed to stabilising the currency with technical measures such as restricting forex swaps and cancelling repo auctions to push up the weighted average cost of funding.
The officials said Qatar's Sheikh Tamin bin Hamad Al Thani pledged to "quickly implement" the investment package during a meeting with Mr Erdogan in Ankara.