Donald Trump appeared to admit his own obstruction of the impeachment investigation against him when he told reporters that "we have all the material" that the administration has withheld from evidence ahead of his trial in the Senate.

After repeating his claims that he did "nothing wrong" and had a "perfect conversation" with Ukrainian president Volodymyr Zelensky, Mr Trump said his legal team "did a very good job" as his trial began on Tuesday.

"But honestly, we have all the material", he said. "They don't have the material".

During a press conference in Davos, Switzerland, where the president is holding court with global leaders at the World Economic Summit, he falsely claimed that Democrats leading his impeachment "don't talk about my conversation" and "they don't talk about my transcripts" that the president believes exonerate him.

The administration released an amended script between the two presidents on a July phone call, at the heart of Mr Trump's impeachment case, in which he is charged with pressuring Mr Zelensky to open an investigation into his political opponent Joe Biden's son, Hunter, who sat on the board of a Ukrainian energy company.

All the president's lawyers: The team fighting Trump's impeachment Show all 6 1 /6 All the president's lawyers: The team fighting Trump's impeachment All the president's lawyers: The team fighting Trump's impeachment Alan Dershowitz Dershowitz is a controversial American lawyer best known for the high-profile clients he has successfully defended. Those clients have included OJ Simpson, Jeffrey Epstein and Harvey Weinstein. One longtime Harvard Law associated told the New Yorker Dershowitz "revels in taking positions that ultimately are not just controversial but pretty close to indefensible." Getty All the president's lawyers: The team fighting Trump's impeachment Ken Starr Starr became a household name in the 1990s as the independent counsel who led the investigation that led to Bill Clinton's impeachment. That investigation began as a look into a real estate scandal known as Whitewater, and eventually led to impeachment after Mr Clinton lied under oath about having an affair with White House intern Monica Lewinsky. AP All the president's lawyers: The team fighting Trump's impeachment Jay Sekulow Sekulow is the president's longtime personal attorney, and, now, personal lawyer in the White House. He has been accused by former Rudy Giuliani associate Lev Parnas of being "in the loop" during the Ukraine scandal. Getty All the president's lawyers: The team fighting Trump's impeachment Pam Bondi Bondi is the former attorney general in Florida, and a longtime backer of the president's. She made a name for herself in Florida for taking hyper partisan stances on issues, and her penchant for publicity. She is likely to be a prominent public-facing figure during the trial. AFP/Getty All the president's lawyers: The team fighting Trump's impeachment Pat Cipollone Cipollone is the White House counsel, and leading the president's defence team. Getty All the president's lawyers: The team fighting Trump's impeachment Rudy Giuliani While not officially named as one of the president's impeachment lawyers, it is hard to ignore Giuliani's outsized role in this process. The former mayor of New York has been making headlines for months as he defends his client, and for his apparent role in the effort to compel Ukraine to launch the investigation into Joe Biden. We'll see how he figures in the actual trial, which he has said he would like to be a part of. Reuters

Mr Trump is charged with abuse of power and obstruction of Congress, after the administration has claimed executive privilege to swat away subpoena requests for documents and has directed officials to ignore requests to testify.

The president also slammed Adam Schiff — who chaired the House Judiciary Committee that pursued the impeachment probe and is now leading the prosecution team against him in the Senate — for creating a "phoney story" that Mr Trump claims is his proof that Democrats lack evidence of his abuse of power.

Mr Schiff's hyperbolic summary of the president's phone call, based on complaints to Congress, preceded the administration's release of an edited transcript of the call.

Mr Trump falsely claimed that "when we released that conversation, all hell broke out with the Democrats, because they said, 'Wait a minute, this is much different than Shifty Schiff told us.'"

During that phone call, Mr Trump reportedly asked Mr Zelensky to investigate the Bidens eight times.

The president told reporters that Democrats "probably didn't think we had transcribers".

He said "the best lawyers in the world have looked at" the call and that the Department of Justice "gave it a sign off".

"All I do is I'm honest", the president said. "I make good deals for my country, and they're honest deals."