White House legal team members mocked the case against President Trump on Tuesday in their first appearance at the Senate impeachment trial, calling out Democrats claiming to have “overwhelming evidence” of wrongdoing but demanding more witnesses and documents.

White House counsel Pat Cipollone said House Democrats are afraid to make their case. He said he would be laughed out of court if he requested more evidence to a judge at the start of a trial.

“Judge, my case is overwhelming — but I’m not ready to go forward. I need more evidence,” he said, mimicking a court appearance. “I would be thrown out in two minutes.

“It’s too much to listen to — the hypocrisy of the whole thing,” he added.

Rep. Adam B. Schiff, California Democrat and the lead House impeachment manager, demanded the opportunity to subpoena more documents and witnesses at the trial’s outset. He said to have a vote on witnesses after each side makes its arguments would be “ass-backward.”

“Any other order makes no sense,” the California Democrat said.

The White House moved to put Mr. Schiff on trial as he stood before the august chamber.

Rebutting Mr. Schiff’s arguments, Mr. Cipollone accused him of falsifying the record for the impeachment inquiry and threatening witnesses.

The president’s counsel referenced Mr. Schiff 97 times in their 110-page brief, setting up the president’s defense against what they say was kangaroo-court impeachment inquiry in the House, where Mr. Trump was denied due process.

“It’s very difficult to sit there and listen to Mr. Schiff tell the tale he just told. Let’s remember how we all got here. They made false allegations about a telephone call,” Mr. Cipollone said.

The president’s lawyer noted Mr. Trump declassified the telephone call in questioning, releasing it to the public.

“When Mr. Schiff saw his allegations were false and he knew it anyway, what did he do? He went to the House and he manufactured a fraudulent version of that call,” Mr. Cipollone said. “He read it to the American people and he didn’t tell them it was a complete fake.”

He said Mr. Schiff selectively leaked information during the House inquiry and threatened witnesses who dared to go to court to assert their constitutional rights.

“What does Mr. Schiff mean by obstructing? He means that unless you do exactly what he says regardless of your constitutional rights then you are obstructing,” Mr. Cippollone said.

He also suggested Mr. Schiff is hiding documents that relate to his staff having communication with the whistleblower, who launched the House impeachment investigation when he filed a complaint about a phone call Mr. Trump had with the president of Ukraine. In the July 25 phone call, the president pressed Ukraine President Volodymyr Zelensky for a “favor” in investigating former Vice President Joseph R. Biden and Ukraine meddling in the 2016 election.

Mr. Schiff has been a central figure in the impeachment and the Democrats’ three-year crusade against Mr. Trump, including promoting the salacious but unsubstantiated dossier that helped spur the Russia collusion probe.

A Ukraine radio show once pranked Mr. Schiff by pretending to be Russians with naked photos of Mr. Trump. Mr. Schiff’s staff pursued the photos until the joke was revealed.

Before the trial convened, the Democrats’ trial managers took on Mr. Cipollone, declaring him a “fact witness” to Mr. Trump’s alleged wrongdoing and demanding he provides testimony.

The said the potential conflict of interest could be severe enough to require his disqualification.

“The ethical rules generally preclude a lawyer from acting as an advocate at a trial in which he is likely also a necessary witness,” they wrote in a letter to the White House. “Even if the advocate does not take the witness stand, his status as an unsworn witness risks seriously damaging the fairness of the trial.”

Their demands previewed the finger-pointing dominating the impeachment fight.

Mr. Trump’s counsel made a similar claim regarding Mr. Schiff, who spearheaded the impeachment and has ties to the White House whistleblower who initiated the impeachment effort.

The White House team previously said Mr. Schiff was a fact witness and questioned his role in the trial.

The two sides also accuse each other of abusing political power to impact the 2020 election.

The showdown over the trial procedure dominated the first day of Mr. Trump’s impeachment trial. Senators and other key players had been sworn in last week, but Tuesday marked the first time the president’s lawyers mounted a defense.

The back and forth over calling witnesses followed weeks of Democrats demanding more evidence for the upper chamber’s hearing. House Speaker Nancy Pelosi held on to the two articles of impeachment — for abuse of power and obstructing Congress — for about a month in an attempt to influence the process.

Senate Majority Leader Mitch McConnell of Kentucky and his Republican conference were united about following the same procedures used for President Bill Clinton’s impeachment trial in 1999, which put off votes on witnesses until later.

The debate continued into the night. The trial rules were expected to pass in a party-line vote.

Back in 1999, the Senate unanimously agreed to the rules for Mr. Clinton.

Mr. McConnell unexpectedly bowed to criticism of his proposal to give each side 24 hours over two days to make their case. That timeline could have extended each trial day until 1 a.m. and prompted critics to label the majority leader “Midnight Mitch.”

The rules resolution offered Tuesday gave each side 24 hours over three days, the same timeline used in Mr. Clinton’s trial.

Mr. McConnell’s office said the change was made after discussions with Republican senators.

Following the 48 hours of arguments, the rules give senators 16 hours to submit written questions.

The issue of witnesses or other new evidence would follow the questions. It would take 51 senators to call a witness.

Republicans hold 53 seats in the upper chamber, while the Democratic caucus controls 47.

Senate Minority Leader Charles E. Schumer, New York Democrat, offered a series of amendments to the rules that would give senators access to White House communications and administration documents.

The first several amendments were shot down in a series of party-line votes.

The party breakdown and the sharp partisan divide on impeachment all but guarantees Mr. Trump will be acquitted in the 100-member chamber, where it takes a supermajority of 67 votes to convict and remove a president from office.

Mr. Trump weighed in on the trial from an economic summit in Davos, Switzerland.

“That whole thing is a hoax,” he said during a bilateral meeting with European Commission President Ursula von der Leyen. “It goes nowhere because nothing happened. The only thing we’ve done is a great job.”

The two previous trials, Mr. Clinton’s and President Andrew Johnson’s in 1868, both ended in acquittals.

Standing at a podium in front of the senators, Mr. Schiff urged them to convict Mr. Trump. He described the two articles of impeachment against Mr. Trump as “the most serious ever charged against a president.”

Mr. Trump’s legal team says he was warranted in his request to the Ukrainian president to probe the Bidens’ conduct given that Hunter Biden, the son of the former vice president, was paid about $50,000 a month to sit on the board of Ukrainian energy company Burisma despite having no expertise in the industry and getting the job while his father was leading Obama administration policy in that graft-riddled country.

Interest increased in Mr. Biden’s actions in Ukraine after he boasted of forcing Ukraine to fire the country’s chief prosecutor in spring 2016. He said he threatened to block a $1 billion U.S. loan guarantee. The prosecutor was widely viewed as not doing enough to combat corruption. But the prosecutor, Viktor Shokin, also had looked into corruption allegations against Burisma and Mykola Zlochevsky, the Ukraine oligarch running the company.

A whistleblower, who is said to be a CIA official assigned to the White House, accused the president of abusing his power on the call, including withholding $391 million of U.S. military aid from Ukraine as leverage.

The whistleblower, whose alleged identity is widely discussed in Washington but whose name is being withheld by The Washington Times, has ties to the Democratic Party and the elder Mr. Biden.

The whistleblower also met with the staff of the chairman for the House Intelligence Committee, Mr. Schiff, for guidance before making the complaint.

Mr. Schiff then spearheaded the impeachment of Mr. Trump and now serves as the lead House manager prosecuting the case in the Senate.

Mr. Trump has acknowledged that he wanted an investigation into alleged corruption involving the Bidens and Ukraine interference in the 2016 election.

Mr. Trump also wanted Ukraine to look into a missing Democratic National Committee server that was hacked by Russia during the 2016 presidential campaigns. An American cybersecurity company called CrowdStrike examined the server to probe the hack but did not have physical control over it. The review was done through imaging. The server disappeared before it got to the FBI.

Mr. Trump subscribes to an unsubstantiated theory that the server ended up in Ukraine.

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