US and Turkish presidents have denied reports Brunson's release was in exchange for US easing economic pressure on Ankara
President Donald Trump said the release and return of pastor Andrew Brunson will be a "tremendous" step toward better relations between the United States and Turkey, where the Christian pastor was detained for two years.
Relations between the two Nato allies have been strained by US support for Kurdish fighters in northern Syria, Turkey's plans to buy a Russian missile defence system, and the US jailing of an executive at a Turkish state bank in an Iran sanctions-busting case, Reuters said.
Brunson, who met with Trump in the Oval Office soon after he arrived in Washington with his wife on Saturday, knelt next to the president in the Oval Office and said a prayer for him.
Brunson, who has become a cause celebre for Trump's conservative Christian base, received a hero's welcome at the White House shortly after his arrival at Joint Base Andrews outside Washington, after being detained for two years in Turkey, AFP reported.
Brunson thanked Trump and his administration, saying "you really fought for us," and later kneeled to pray for the president, his hand on Trump's shoulder.
Trump repeatedly thanked Turkish President Recep Tayyip Erdogan for his help on the case, which caused not only a serious diplomatic row between the Nato allies but led to a crash in the lira, exposing Turkey's economic fragility.
"It's not an easy situation for Turkey either. They had a lot of difficult situations going on, and I do want to thank President Erdogan for making this possible," Trump said.
There was NO DEAL made with Turkey for the release and return of Pastor Andrew Brunson. I don’t make deals for hostages. There was, however, great appreciation on behalf of the United States, which will lead to good, perhaps great, relations between the United States & Turkey!
— Donald J. Trump (@realDonaldTrump) October 13, 2018
Earlier on Saturday, Trump had tweeted: "There was NO DEAL made with Turkey for the release and return of Pastor Andrew Brunson. I don’t make deals for hostages."
He followed that with: "There was, however, great appreciation on behalf of the United States, which will lead to good, perhaps great, relations between the United States & Turkey!"
On Friday, a Turkish court in the western port city of Aliaga convicted Brunson on charges of espionage and aiding terror groups. It sentenced him to three years, one month and 15 days in jail but released him based on time served and good behaviour.
Erdogan has said the court's decision was "taken independently".
Both Erdogan and Trump have denied reports that the two sides reached a secret deal for the 50-year-old Brunson to be released in exchange for the US easing "economic pressure" on Ankara.
Erdogan later responded: "I hope that the United States and Turkey continue cooperation in a manner that befits two allies."
— Anthony Sottasante (@asottasante70) October 13, 2018
Brunson is an evangelical Presbyterian clergyman who lived in Turkey for almost half his life, initially moving there in 1993 as part of a missionary programme.
He was first detained in October 2016 and faced as many as 35 years in jail. Prosecutors then demanded a sentence of up to 10 years. The pastor steadfastly insisted he was not guilty.
"I am an innocent man. I love Jesus. I love Turkey," he said in his final defence.
When the verdict was read out, Brunson wept and hugged his wife Norine.
After gathering his belongings, Brunson was driven to the airport in the Turkish city of Izmir, where he boarded a US military plane for Germany.
Upon arrival there for a refuelling stop, he kissed an American flag presented to him by Richard Grenell, the US ambassador in Berlin.
President Donald Trump to American pastor Andrew Brunson, who was released after being detained in Turkey for two years: "You are very, very special to all of us" pic.twitter.com/aIlyBlcPgf
— CNN Politics (@CNNPolitics) October 13, 2018
While the strain in US-Turkish relations eased with Brunson's release, problems remain.
Secretary of State Mike Pompeo urged Turkey to "quickly release" other Americans in detention.
He said Washington would "continue to work hard to bring home all American hostages and those wrongfully imprisoned and detained".
Nasa scientist Serkan Golge, a dual US-Turkish national, was jailed for seven and a half years in February on terror charges, a term reduced to five years last month.
And two Turkish employees of US diplomatic missions remain in jail. One of them, former Adana consulate staffer Hamza Ulucay, was denied release on Friday.
Anthony Skinner, director for the Middle East and North Africa at the Verisk Maplecroft consultancy, said that the US and Turkey had plenty of disagreements beyond Brunson.
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"The clamp has now been removed, which opens the way for bilateral negotiations to address other sources of disagreement, but Washington and Ankara still have to navigate through a minefield," Skinner said.
He pointed to Turkey's order for Russian S-400 missile defence systems, which has riled its Western allies, as well as Ankara's determination to do business with Iran in defiance of US sanctions.
Turkey is bracing for potential fines from US authorities over sanctions-busting by Turkish lender Halkbank, whose deputy director general has been jailed in the United States.
Brunson's release comes at a sensitive time for the Turkish leadership, which is under global scrutiny over how it handles the case of Saudi journalist Jamal Khashoggi, who disappeared at Riyadh's consulate in Istanbul on 2 October.
Both Erdogan and Trump have pressed Saudi Arabia to explain what happened to Khashoggi.
Now that the Brunson issue has been resolved to Washington's satisfaction, it may help the two sides coordinate their Saudi policy more closely.