Lindsey Graham and Jeanna Shaheen said Recep Tayyip Erdogan and "receptive" during their "candid" meeting on Friday - which also discussed the sale of fighter jets.
Mr Graham, the Republican representative for South Carolina wrote on Twitter: "Very good, respectful, and candid meeting with President Erdogan.
"We have real differences, but far more in common. Turkey needs to be a strategic partner for the US in a win-win fashion.
"We spoke candidly about Pastor Brunson and other friction points, including the purchase of Russian made S-400s and American made F-35s.
"However, when it comes to the US-Turkey relationship, failure is not an option."
Andrew Brunson (pictured above with his wife, Norine), who had been living in Turkey for more than 20 years prior ro his arrest in October 2016, is currently on trial after being charged with "membership in an armed terrorist organization."
The 50-year-old leader of Izmir Dirilis (Resurrection) Church - a small evangelical Presbyterian congregation in the city of Izmir - faces up to 35 years in prison.
Democrat representative for New Hampshire, Jeanne Shaheen wrote on Twitter : "I'm in Turkey to help build a constructive dialogue with President Erdogan on the cases of Americans wrongfully arrested and other issues of mutual concern.
"President Erdogan was receptive to my and Lindsey Graham's concerns."
Shasheen was recently among a number of senators who drafted a bill trying to block the sale of F-35 fighter jets by the US to Turkey in protest at Brunson's detention and Ankara's decision to buy missiles from Russia.
Mr Brunson, who comes from Black Mountain in North Carolina, denies involvement with the Gülen movement, an organisation which Turkey blames for a failed bid to overthrow its government in July 2016.
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