President Trump tore into House Democrats' ongoing impeachment inquiry Wednesday during a press conference with Turkey President Recep Tayyip Erdogan, decrying the hearsay-laden "witch hunt" and saying he hadn't watched that day's public hearing "for one minute."

"This is a sham, and shouldn't be allowed -- it was a situation that as caused by people who couldn't have allowed it to happen. I want to find out who's the whistleblower," the president said, claiming that the whistleblower behind the impeachment inquiry has made provably inaccurate statements.

"I'm going to be releasing, I think on Thursday, [another] transcript, which actually was the first of the two [phone calls with Ukraine's leader]," he said.

The White House has already released a transcript of Trump's July 25 call with Ukraine's president, in which the two discussed past U.S. "support" for Ukraine, as well as Ukraine's issues with corruption. On the call, Trump asked Ukraine to investigate reports that Ukraine was involved in 2016 election interference. The president also mentioned Joe Biden's push to have Ukraine's chief prosecutor fired, and suggested the country look into the matter.

Asked at the press conference about acting ambassador to Ukraine Bill Taylor's testimony about an alleged July 26 phone call between the president and U.S. envoy to the European Union Gordon Sondland, Trump said: "I know nothing about that -- first time I've heard it."

Taylor testified, for the first time, that the president was overheard by a member of his staff on July 26 asking Sondland about “the investigations,” to which Sondland responded that “the Ukrainians were ready to move forward.” Taylor said that following Sondland’s call with Trump, the member of his staff asked what Trump thought about Ukraine.

“Ambassador Sondland responded that President Trump cares more about the investigations of Biden, which Giuliani was pressing for,” Taylor said, revealing new information from his prior testimony last month. “At the time I gave my deposition on October 22, I was not aware of this information. I am including it for completeness.”

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At the press conference, the president pointed to Sondland's written testimony: "The one thing I've seen that Sondland said, he did speak to me for a brief moment, he did speak to me for a brief moment -- [he testified previously that] I said, no 'quid pro quo,' under any circumstances. And that's true. In any event, it's more second-hand information. ... The only thing, and I guess Sondland has stayed with his testimony, that there was no quid-pro-quo, pure and simple."

Trump added that witnesses summoned by Democrats during the impeachment hearings had produced "all third-hand information" and unreliable hearsay. "This statement that I made, the whole call that I made with the president of Ukraine, was a perfect one. ... I'd much rather focus on peace in the Middle East."

Despite a BBC report that Erdogan had recently thrown a letter from Trump in the trash, Erdogan began the news conference by telling reporters Trump was a "good friend." Trump reciprocated, calling the autocrat a "great president" and claiming that Turkey had a "great relationship with the Kurds."

Erdogan announced that between six months to two years from now, Turkey could repatriate about one million refugees into a safe zone established in northern Syria. Outside the White House, dozens of Kurds and their supporters waved Kurdish and American flags in protest.

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The press conference came after the two leaders met in the White House, and followed a meeting with five Republican senators, including Ted Cruz of Texas and Lindsey Graham of South Carolina. (After Trump urged his Erdogan to call on “a friendly reporter from Turkey," Graham reportedly turned to an ABC News reporter to remark, “There aren’t any others left.” The president joked afterward that the Turkish reporter Erdogan called on appeared to work for the Turkish government.)

In a statement late Wednesday, Graham vowed that the United States "cannot and will not abandon our Syrian Democratic Forces (SDF) allies," and added: "I realize Turkey has legitimate national security concerns regarding certain Kurdish elements of the U.S.-led counter-ISIS coalition, but Turkey’s incursion into Syria has been incredibly disruptive. I believe it is possible to deal with Turkey’s national security concerns by creating a Safe Zone, but Turkey cannot do it through force of arms.

“As to Turkey’s purchase of the S-400 Russian missile system: it is almost a universally held position in Congress that the S-400 is incompatible with the F-35 fighter," Graham continued. "Turkey’s activation of the Russian S-400 will require the U.S. to keep Turkey from the F-35 program and issue sanctions. I’m hopeful we can find a way forward with the S-400 where Turkey’s national security needs can be met without compromising the F-35 program."

Erdogan and Trump had a difficult agenda for their talks, which included Turkey's decision to buy a Russian air defense system despite Ankara's membership in NATO and its incursion into neighboring Syria to attack Kurdish forces that have fought with the U.S. against the Islamic State (ISIS) group.

Despite those disputes, Trump said the two countries were poised to agree to increase U.S. goods and services trade with Turkey, which totaled about $24 billion in 2017.

Trump defended his decision to invite Erdogan despite Turkey’s widely denounced advance into Syria. He said that he and Turkey’s president have been “very good friends” for a long time and understand each other’s country.

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“We’re going to be expanding,” Trump said. “We think we can bring trade up very quickly to about $100 billion between our countries.”

The president was "pleased" that Turkey was increasing spending on its own defense, and noted that other NATO allies have been lagging behind.

"I know that the ceasefire, while complicated, is moving forward -- and moving forward at a very rapid clip," Trump said, later adding that Turkey's acquisition of advanced Russian military equipment presents "serious challenges."

Republican lawmakers have pressed Erdogan about why Turkey bought the S-400 Russian air defense missile system. The U.S. and fellow NATO nations say the S-400 would aid Russian intelligence and compromise a U.S.-led fighter jet program.

The U.S. has since kicked Erdogan out of a multinational program producing components of America's high-tech F-35 fighter jet. In response, Erdogan attended an air show this summer in Moscow and expressed interest in buying the latest Russian Su-35 fighter jets.

"We have a lot of trade with Turkey, but it could be many times higher ... We intend to bring it up to about $100 billion, which would be about four times what it is now," Trump said.

Trump also said Turkey has been helping the U.S. "a lot" in fighting ISIS.

Meanwhile, in the Senate, two Democrats introduced legislation denouncing Turkey's targeting of journalists, political opponents, dissidents, minorities and others. They said the Turkish government has imprisoned more than 80,000 Turkish citizens, closed more than 1,500 nongovernmental organizations on terrorism-related grounds and dismissed or suspended more than 130,000 civil servants from their jobs.

In October, Trump moved U.S. forces out of the way of invading Turkish troops, a decision that critics said amounted to abandoning America's Kurdish allies, but that Trump defended as an important end to an otherwise "endless" military engagement in the Middle East.

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Trump administration officials have said Trump told Turkey not to invade Syria. But when Erdogan insisted, they say, Trump decided to move 28 Green Berets operating on the Turkey-Syria border so they wouldn't be caught in a crossfire between Turkish-backed forces and the Kurds.

"I think a tremendous amount of progress is being made," Trump said.

Fox News' Chad Pergram and The Associated Press contributed to this report.