US President Donald Trump's impeachment trial has begun in earnest in the Senate, with his chief legal defender attacking the case as baseless while a top Democratic politician described overwhelming evidence of wrongdoing.

Democrats have called on the Republican-controlled Senate to remove Mr Trump from office for pressuring Ukraine to investigate former Vice President Joe Biden, a political rival, and then obstructing an inquiry into the matter.

Mr Trump, who was impeached last month by the Democratic-led House of Representatives on charges of abusing power and obstructing Congress, denies any wrongdoing.

He has described his impeachment as a partisan hoax to derail his 2020 re-election.

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With the television cameras rolling, US Supreme Court 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 Mr Trump's defence, attacked the foundation of the Democrats' charges against the Republican president and said they 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," Mr Cipollone said as he argued in favour of Mr McConnell's proposal to decide on whether to allow further witnesses or documents later in the trial.

"There is absolutely no case," he said.

Democratic Representative Adam Schiff, who helped spearhead the House impeachment inquiry, summarised the charges against Mr Trump and said the Republican president had committed a "trifecta of constitutional misconduct justifying impeachment."

Mr Schiff said that although the evidence against Mr Trump was "already overwhelming," further witness testimony was necessary to show the full scope of the misconduct of the president and those around him.

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

Mr McConnell unveiled a plan yesterday for what would be a potentially quick trial without new testimony or evidence.

It would give House Democratic prosecutors and Mr Trump's lawyers 48 hours, evenly split, to present their arguments over four days.

That plan has now been changed to give each side three days of opening arguments over two 24-hour periods.

The rules also will allow the House's record of the impeachment probe admitted as evidence in the trial, as Democrats had demanded.

A spokesman for Mr McConnell said the changes were made after discussions in a closed-door lunch for Republican senators.

Democrats had accused Mr McConnell of trying to rig a trial with proposed rules that they said would prevent witnesses from testifying and bar evidence gathered by investigators.

Mr McConnell has repeatedly said the rules would mirror those the Senate used in the 1999 impeachment of then-president Bill Clinton, a Democrat.

Republican senators have not ruled out the possibility of further witness testimony and evidence.

With a two-thirds majority needed in the 100-member Senate to remove Mr Trump from office, he is almost certain to be acquitted by fellow Republicans in the chamber.

However the impact of the trial on his re-election bid is far from clear.