President Trump invited Mr Brunson to the White House to celebrate his release from nearly two years of confinement, from which he was freed on Friday.
"From a Turkish prison to the White House in 24 hours, that's not bad," Trump said.
Brunson left Turkey immediately, had a medical check-up in Germany and then returned to the US aboard a military jet shortly before meeting the president.
As part of a press conference, the evangelical pastor from Izmir Resurrection Church in Turkey, asked if he could pray for the US President.
The president replied, "Well, I need it probably more than anyone else in this room, so that would be very nice, thank you."
Brunson left his chair beside Trump, kneeled and placed a hand on the president's shoulder.
As Trump bowed his head, Brunson prayed: "God, I ask that you pour out your Holy Spirit on President Trump, that you give him supernatural wisdom to accomplish all the plans you have for this country and for him. I ask that you give him wisdom in how to lead this country into righteousness.
"I ask that you give him perseverance, and endurance and courage to stand for truth. I ask that you to protect him from slander from enemies, from those who would undermine. I ask that you make him a great blessing to this country. Fill him with your wisdom and strength and perseverance. And we bless him. May he be a great blessing to our country. In Jesus' name, we bless you. Amen."
Norine, Andrew's wife then prayed as well: "I just want to pray that the Spirit of the Lord will rest on the President, the spirit of wisdom and understanding, the spirit of counsel and light, the spirit of knowledge and fear of the Lord, Amen."
The president then said: "Thank you very much, can I ask you one question? Who did you vote for?"
The room laughed as Trump suggested he knew the answer and Brunson just replied: "I would like to say I sent in an absentee ballot from prison".
Trump also addressed the rumour that there was a deal for Brunson's freedom with Turkey.
"We do not pay ransom in this country," Trump said.
He thanked Turkey's president, Recep Tayyip Erdogan, who had declined the demands of Trump and other high-level US officials for Brunson's release.
The US had repeatedly called for Brunson's freedom and, this year, sanctioned two Turkish officials and doubled tariffs on steel and aluminium imports citing in part Brunson's plight.
Trump said the US greatly appreciated Brunson's release and said the move "will lead to good, perhaps great, relations" between the US and fellow Nato ally Turkey, and said the White House would "take a look" at the sanctions.
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