Mr Pence tweeted: “Pastor Andrew Brunson is an innocent man held in Turkey & justice demands that he be released.
“Turkey would do well not to test @POTUS Trump’s resolve to see Americans who are wrongfully imprisoned in foreign lands returned home to the United States.”
The two NATO allies have exchanged tit-for-tat sanctions over the pastor’s house arrest.
Turkey’s currency, which had been under pressure as inflation soars, plunged more than 20% last week after Mr Trump imposed sanctions on Turkey’s steel and aluminium exports.
However, the Turkish lira has staged a recovery as Turkey hit back with its own tariffs and made it more difficult for investors to short the currency.
It also won support from Qatar, which plans to invest $15bn in Turkey.
There were fears Ankara may need to turn to the International Monetary Fund as the currency crisis escalated.
The lira, which has fallen almost 40% against the dollar this year, rose 4.5% to 5.7TL on Thursday afternoon.
Finance minister Berat Albayrak told more than 3,000 international investors and economists on a video conference that Turkey would emerge stronger from the crisis.
Mr Albayrak, President Recep Tayyip Erdogan’s son-in-law, said the country’s banks were healthy and strong and the nation would not be turning to the IMF.