Istanbul, Turkey (CNN) Recep Tayyip Erdogan denied Sunday that Turkey had agreed to free a detained American pastor as part of a possible deal with the US and Israel, and warned that Turkey would not be bullied into releasing him by US President Donald Trump.

The Turkish President's comments come after a senior US official told CNN last week that Erdogan and Trump had agreed to a deal that would see Israel release an imprisoned Turkish national in exchange for Turkey freeing Andrew Brunson, who has been held in Turkey since October 2016.

The Turkish national, Ebru Ozkan, was allowed to leave Israel for Turkey in mid-July. Brunson, meanwhile, was released into house arrest on Wednesday but has not been permitted to leave Turkey.

On Thursday, Trump threatened Turkey with retaliation, tweeting: "The United States will impose large sanctions on Turkey for their long time detainment of Pastor Andrew Brunson, a great Christian, family man and wonderful human being. He is suffering greatly. This innocent man of faith should be released immediately!"

I spoke yesterday with Turkey's Foreign Minister @MevlutCavusoglu and underscored that it is well past time for this innocent Pastor Andrew Brunson to come home. pic.twitter.com/6zU8pw0P0A

Erdogan insisted Sunday that no deal had taken place.

"We told the Americans that they could help us with getting Ebru (Ozkan) ... but we never said 'and in exchange we will give you Brunson,'" Erdogan told state broadcaster TRT. "We never made Brunson a topic of negotiation. Instead of respecting the Turkish judiciary, they are turning this into talk of sanctions."

Erdogan warned the US it risked losing a "strong and sincere partner" if it did not change its attitude.

"You cannot make Turkey take a step back with sanctions," Erdogan added. "They need to know the following: we are not tied with an umbilical cord to the US."

"The change in attitude is Trump's problem, not mine," Erdogan added.

The White House did not immediately respond to requests for comment on Sunday.

Deal or no deal?

The senior US official told CNN that the deal to free Brunson -- an evangelical Presbyterian pastor from North Carolina -- was agreed to by Trump and Erdogan during a meeting at the NATO summit in mid-July.

Days after that meeting, Trump asked Israeli Prime Minister Benjamin Netanyahu to assist in the pastor's release, an Israeli official told CNN. While the official would not divulge details of their conversation, or when the request took place, the two leaders spoke on the phone on July 14.

Ozkan, a 27-year-old Turkish woman held in Israel on suspicion of aiding Hamas, the Palestinian militant group that controls Gaza, was released from prison between July 11-12, her lawyer told CNN.

She was able to leave Israel for Turkey on July 15, one day after Trump spoke with Netanyahu. In an extremely unusual move, Israeli prosecutors had permitted Ozkan -- who faces terror-related charges -- to leave the country two weeks before her trial, effectively freezing the case against her. But the charges against her were not dropped.

Brunson was arrested in 2016 during the Turkish government's crackdown following an attempted coup. In March, he was formally charged with espionage and having links to terrorist organizations. If convicted, he faces up to 35 years in prison. He maintains his innocence.

On July 18 -- three days after Ozkan flew back to Turkey -- a Turkish court rejected an appeal by Brunson's lawyers to have him freed.

Then, on Wednesday, Brunson was released to house arrest and ordered to wear an electronic monitoring device.

The following day, Trump launched his Twitter tirade against Turkey.

The United States will impose large sanctions on Turkey for their long time detainment of Pastor Andrew Brunson, a great Christian, family man and wonderful human being. He is suffering greatly. This innocent man of faith should be released immediately! — Donald J. Trump (@realDonaldTrump) July 26, 2018

Pence echoed Trump's stance during remarks at the State Department on Thursday.

"If Turkey does not take immediate action to free this man of faith and send him home to America, the United States will impose significant sanctions on Turkey until Pastor Andrew Brunson is free," Pence said. "While he is out of jail he is still not free."

Secretary of State Mike Pompeo has spoken to Turkish Foreign Minister Mevlut Cavusoglu several times over the past few days in an effort to secure Brunson's freedom.

A senior Turkish official denied Friday that there was any connection between the release of Ozkan and the case of Brunson, describing the claims as "completely baseless."

Erdogan: Give us our F-35s

Erdogan also said Sunday that Turkey would resort to international arbitration -- possibly referring to an international court -- if the US doesn't deliver the F-35 fighter jets it purchased.

"Now they've started threatening us with one more thing. They say they may not give us the F-35s. We told them we'll go to international arbitration," Erdogan said.

Although Turkey has long been a participant in the development of the F-35 program -- investing $1.25 billion in the project since 2002 -- US lawmakers have sought to block Turkey from receiving the stealth warplanes amid a deterioration of the US-Turkey relationship and concerns over Ankara's purchase of a Russian-made anti-aircraft system.

Turkey technically took ownership of its first F-35s in June, but the US has retained custody of the jets while Turkish pilots and maintainers are being trained on the new planes at Luke Air Force Base in Arizona.

Turkey plans to eventually acquire 100 F-35s.