The announcement follows Turkish President Recep Tayyip Erdoğan's call for a boycott of USA electronics, including Apple's iPhones to counter Trump's actions to ramp up pressure on Turkey to release Brunson.
Trump has repeatedly tweeted his support for Brunson, describing him as a "fine gentleman", a "Christian leader in the United States" and a "respected USA pastor" whose continued holding by Turkey was a "total disgrace".
The Turkish officials did not provide any further information on the nature of the investments, according to AP.
Only weeks ago it would have seemed fanciful to draw a link between the fate of an American pastor in Turkey, a crisis between two North Atlantic Treaty Organisation allies and turmoil on global financial markets.
The rebound of around six percent on Wednesday, briefly strengthening to less than 6.0 against the dollar, came after the central bank squeezed lira liquidity in the market, effectively pushing up rates and supporting the currency.
The Turkish lira plummeted to a record low on Monday, losing almost 40 percent of its value since the start of 2018.
Turkey announced Wednesday it is increasing tariffs on imports of certain USA products, escalating a feud with the United States that has helped trigger a currency crisis. The Turkish lira sank to a fresh to low of 7.24 to the dollar in early Asia Pacific trade last Monday.
"The import duties were increased on some products, under the principle of reciprocity, in response to the U.S. administration's deliberate attacks on our economy", Oktay wrote on Twitter.
Brunson was in prison for 20 months and recently was released to house arrest.
But Andrew Brunson, a Protestant clergyman who had lived in Turkey for a quarter of a century without disturbance, is now at the centre of a bitter row pitting Washington against Ankara that caused the lira to crash and the economic jitters to spread globally. Global investors have been put off by the country's high levels of foreign debt and Erdogan's refusal to allow the central bank to raise interest rates to support the currency, as experts say it should.
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The lira´s fall had raised fears Turkey was on the verge of a fully-fledged economic crisis, especially in its banking system, that could spill over into Europe and other markets.
He was arrested in October 2016 during the purges occurring after the aftermath of the 2016 Turkish coup d'état attempt, which involved imprisoning tens of thousands of Turkish military personnel, civil servants, educators, academics, dissidents, and journalists.
The two sides discussed Erdogan's upcoming visit to Berlin slated for late September, and a meeting between Turkey's Treasury and Finance Minister Berat Albayrak and Germany's Economy Minister Peter Altmaier, due to be held in coming days.
Qatar has pledged to invest $15bn (£11.8bn) in Turkey as Ankara rolls out measures to strengthen the lira amid a trade spat with the US.
It was also helped by a step from the banking watchdog BDDK, cutting the limit for Turkish banks' forex swap, spot and forward transactions with foreign banks to 25 per cent of a bank's equity.
That fueled a relatively high rate of economic growth-7 percent past year.
The lira firmed as far as 5.75 against the dollar on Wednesday and stood at 6.08 at 0943 GMT in a move initially triggered by the Turkish court decision on the Greek soldiers who faced espionage charges.
There was no resolution to the Brunson case in sight.
Erdoğan and Trump are locked in a dispute about the U.S. pastor Andrew Brunson, who was arrested nearly two years ago and accused of plotting against the Turkish government. An upper court had yet to rule on the appeal, his lawyer told Reuters.
When asked about the tariffs impact on the Turkish currency, she said Washington is "monitoring the situation".