The Republican-controlled United States Senate rejected three Democratic efforts on Tuesday to obtain documents and evidence in President Donald Trump's impeachment trial, an early sign the proceeding could advance along lines favourable to Trump.

As the third impeachment trial in US history began in earnest, senators voted 53-47 along party lines to block three separate motions from Democratic leader Chuck Schumer to subpoena records and documents from the White House, the State Department and the Office of Management and Budget related to Trump's dealings with Ukraine.

After the third vote, Schumer introduced a motion seeking the testimony of acting White House Chief of Staff Mick Mulvaney.

Democrats have called on the Senate to remove Trump from office for pressuring Ukraine to investigate former Democratic Vice President Joe Biden, a political rival, and then impeding the inquiry into the matter.

Trump, who was impeached last month by the Democratic-led House of Representatives on charges of abusing power and obstructing Congress, denies any wrongdoing and describes his impeachment as a partisan hoax to derail his 2020 re-election effort.

During the early debate, Trump's chief legal defender attacked the case as baseless and a top Democratic lawmaker said there was "overwhelming" evidence of wrongdoing.

With the television cameras rolling, US Chief Justice John Roberts convened the proceedings and the two sides began squabbling over Senate Majority Leader Mitch McConnell's proposed rules for the trial.

White House counsel Pat Cipollone, who is leading Trump's defence, attacked the foundation of the charges against the Republican president and said Democrats had not come close to meeting the US constitution's standard for impeachment.

"The only conclusion will be that the president has done absolutely nothing wrong," Cipollone said as he argued in favour of McConnell's proposal to decide on whether to allow further witnesses or documents later in the trial.

"There is absolutely no case," he said.

Democrats seek testimony

Democratic Representative Adam Schiff, who helped spearhead the House impeachment inquiry, summarised the charges against Trump and said the president had committed "constitutional misconduct justifying impeachment". Schiff said that although the evidence against Trump was "already overwhelming", further witness testimony was necessary to show the full scope of the misconduct by the president and those around him.

Democrats want a number of current and former Trump administration officials, including Trump's former national security adviser John Bolton, to testify.

"For all of the name-calling and finger-pointing from the president's counsel, we did not hear a single argument on the merits about why there should not be the documents and witnesses we requested in this trial," Schumer said.

Republican senators have not ruled out the possibility of further witness testimony and evidence, with likely votes later in the trial after days of opening arguments and senators' questions.

McConnell unveiled a plan on Monday for what would be a potentially quick trial without new testimony or evidence. It would have given Democratic prosecutors and Trump's lawyers 48 hours, evenly split, to present their arguments over four days.

That plan was changed to give each side three days to give opening arguments. The rules also will allow the House's record of the impeachment probe to be admitted as evidence in the trial, as Democrats had demanded.

Democrats had accused McConnell of trying to rig a trial with proposed rules they said would prevent witnesses from testifying and bar evidence gathered by investigators. McConnell has repeatedly said the rules would mirror those used in the 1999 impeachment of then-President Bill Clinton, a Democrat.

Under McConnell's plan, lawyers for Trump could move early in the proceedings to ask senators to dismiss all charges, according to a senior Republican leadership aide, a motion that would likely fall short of the support needed to succeed.

Even if such a motion fails, Trump is almost certain to be acquitted by the 100-member chamber, where a two-thirds majority is needed to remove him from office.

But the impact of the trial on his re-election bid in November is far from clear.

Trump support firm

Democrats accuse Trump of pressuring Ukraine, a vulnerable ally, to interfere in US elections at the expense of American national security and say he is a danger to American democracy.

Trump and his legal team say there was no pressure and that the Democrats' case is based on hearsay.

Cipollone described the Ukraine investigation as an illegal attempt to remove a democratically elected president and avert his re-election.

"They're not here to steal one election, they're here to steal two elections," Cipollone said.

The White House defence team also repeated some false charges. Cipollone said Republicans were excluded from the secure facility where the initial depositions for the House impeachment hearings took place, when Republican members of the House Intelligence Committee were not only present but questioned witnesses.

Trump's lawyer Jay Sekulow said the White House was not allowed to have a lawyer present during the impeachment hearings, when in fact it declined to participate.

The Senate trial is expected to continue six days a week, Monday through Saturday, until at least the end of January.

Trump has sought to rally his base with the impeachment issue, fundraising off it. At raucous election rallies, he has painted himself as the victim of a witch hunt.

Televised congressional testimony from a parade of current and former officials who spoke of a coordinated effort to pressure Ukraine to investigate the Bidens has done little to change support for and against Trump's impeachment. Reuters/Ipsos polling since the inquiry began shows Democrats and Republicans responding largely along party lines.

Markets shrug off trial

Financial markets have shrugged off the impeachment trial, and the disclosures in the months-long impeachment investigation have done little to boost anti-Trump sentiment among undecided voters or shift away moderate Republican voters.

No president has ever been removed through impeachment, a mechanism the nation's founders — worried about a monarch on American soil — devised to oust a president for "treason, bribery or other high crimes and misdemeanours".

A pivotal event in the impeachment case is a July 25 phone call in which Trump asked Ukrainian President Volodymyr Zelenskiy to investigate the Bidens and a discredited theory that Ukraine, not Russia, meddled in the 2016 US election.

Hunter Biden had joined the board of Ukrainian energy company Burisma while his father was vice president. Trump has accused the Bidens of corruption without offering evidence. They have denied wrongdoing.

Democrats said Trump abused his power by initially withholding $391 million in Ukraine security aid intended to fight Russia-backed separatists, and a coveted White House meeting for Zelenskiy, to pressure Ukraine to announce the investigations of the Bidens. Trump's legal team says there is no evidence that the aid was a condition for receiving help.

The obstruction of Congress charge relates to Trump directing administration officials and agencies not to comply with House subpoenas for testimony and documents related to impeachment.