Democrats worked methodically at United States President Donald Trump's impeachment trial on Thursday to dismantle his long-standing allegation that Democratic presidential contender Joe Biden acted improperly towards Ukraine while vice president.

On the second day of their arguments for Trump's removal from office, Democratic House of Representatives members acting as prosecutors argued that Biden was carrying out official US policy when he pressured Ukraine to fire its top prosecutor, Viktor Shokin, because of corruption concerns.

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Trump and his allies maintain that Biden wanted Shokin out in order to head off an investigation into a natural gas company, Burisma, where his son Hunter served as a director. Democrats said no evidence supported that allegation.

Democrats argued, instead, that Trump pushed the Ukrainian government to probe Biden and his son because he was worried about facing the former vice president in November's election. Biden is the frontrunner for the Democratic presidential nomination.

"There was no basis for the investigation that the president was pursuing and pushing. None. He was doing it only for his own political benefit," US Representative Sylvia Garcia said on the Senate floor.

Democrats contend senators should convict Trump on two charges brought by the Democratic-led House - abuse of power and obstruction of Congress.

But the Senate, which is controlled by Trump's fellow Republicans, remains unlikely to do so. A two-thirds majority is needed to remove him from office.

Lead manager House Intelligence Committee Chairman Adam Schiff delivers an opening argument in the US Senate Chamber [US Senate TV/Reuters]

The US Constitution sets out the impeachment process for removing a president who commits "high crimes and misdemeanours". Trump's legal team has argued that the House charges were invalid because impeachable offences must represent a specific violation of criminal law.

Trump condemned the proceedings as "unfair & corrupt" in a Twitter post on Thursday.

The charges against Trump arise from his request in a July 25 phone call last year that Ukraine investigate Biden on unsubstantiated corruption allegations and the president's actions to impede a House inquiry into the matter.

Trump also asked Ukrainian President Volodymyr Zelenskyy to investigate a discredited theory beneficial to Russia that Ukraine worked with Democrats to hurt Trump in the 2016 US election. Trump temporarily withheld $391m in US military aid to Ukraine, which Democrats say was leverage for his demands.

'Opened the door'

Trump's lawyers quickly argued that by bringing up the Bidens, Democrats had made their conduct a relevant subject for the rest of the trial.

"They opened the door. They opened the door and it's now relevant," Jay Sekulow, a personal lawyer for the president and a member of his defence team, told reporters at the Capitol. "So we will address the appropriate issues as defence lawyers would."

Trump's lawyers are likely to begin their defence of the president on Saturday after House Democrats finish their opening arguments.

Trump's personal lawyer Jay Sekulow speaks to the media during a break in the impeachment trial of Trump [Jacquelyn Martin/AP Photo]

Some Republicans have floated the idea of getting one or both of the Bidens to testify next week in exchange for witnesses like former National Security Advisor John Bolton. Democrats have dismissed the prospect, saying it would only give legitimacy to baseless conspiracy theories.

"These are what we call irrelevant, not relevant witnesses. Distractions is another word," said Democratic Senator Mazie Hirono.

Speaking on the Senate floor, Garcia argued Trump did not pressure Ukraine to investigate corruption and had supported sending military aid to the country until Biden announced his presidential bid in early 2019.

She pointed out that in the months before Trump asked Ukraine to investigate the Bidens, polls had been showing that Biden would beat Trump in a presidential matchup. In May, she said a Fox News poll showed Biden beating Trump by 11 points.

"This clearly did not go unnoticed," she said.

Garcia also poured cold water on a conspiracy theory offered by some Trump defenders that Ukraine, not Russia, had interfered in the 2016 US election.

"If this sounds far-fetched and crazy, it should, because it is," Garcia said.

US intelligence agencies and former Special Counsel Robert Mueller concluded that Russia used a campaign of hacking and social media propaganda to interfere in the election to sow discord in the US and boost Trump's candidacy against Democrat Hillary Clinton. Moscow has denied meddling in the election.

The Democrats displayed a November quote from Russian President Vladimir Putin saying: "Thank God nobody is accusing us any more of interfering in the US elections. Now they're accusing Ukraine."

Restless days

Signs emerged on the second day of arguments that the Democratic case was losing some of the public's attention. There were empty seats in the gallery overlooking the Senate floor.

Television ratings were down. About 8.9 million viewers watched the first day of arguments on Wednesday, falling short of the roughly 11 million who watched on Monday, according to Nielsen ratings data.

Senators also showed increasing signs of restlessness, with many wandering to the rear of the chamber where they could make phone calls and check their smartphones.

Republican Senator Richard Burr handed out fidget spinners, small toys designed to be spun between the fingers, to his colleagues before Thursday's trial proceedings began.

Burr was seen playing with a blue spinner while listening to arguments by House manager Jerrold Nadler Other senators, including Republicans Tom Cotton and Pat Toomey were also seen with spinners on their desks.

While it remains a long shot for Democrats to secure Trump's removal through impeachment, the trial gives them a venue to inflict political damage on him in the run-up to the November election, with millions of Americans watching the televised proceedings.

Before Thursday's arguments began, some Republican senators said they had heard nothing new in the presentation made by the Democratic managers and had already decided to vote for acquittal.