The claim came as the Democrats pressed their case for a second day before sceptical Republican Senate jurors at the president’s impeachment trial.
The Democrats displayed video images of the nation’s top FBI and Homeland Security officials warning the public off the theory it was Ukraine, not Russia, that interfered in the 2016 election.
“That’s what Donald Trump wanted investigated or announced — this completely bogus Kremlin-pushed conspiracy theory,” said Representative Adam Schiff, the chairman of the House Intelligence Committee who is leading the prosecution.
Mr Trump is accused of seeking the investigation — and probes of political foe Joe Biden and Mr Biden’s son — for his own political benefit while holding back Congress-approved military aid as leverage.
“You can imagine what a danger that presents to this country,” Mr Schiff told the hearing.
Mr Trump is facing trial in the Senate after the House impeached him last month, accusing him of abusing his office by asking Ukraine for the investigations while withholding the aid from a US ally at war with bordering Russia.
The president faces a second article of impeachment accusing him of obstructing Congress by refusing to turn over documents or allow officials to testify in the House investigation.
Republicans, growing tired of the long hours in the first days of proceedings, have defended Mr Trump’s actions as appropriate and cast the process as a politically motivated effort to weaken him in the midst of his reelection campaign.
Republicans hold a 53-47 majority in the Senate, and acquittal is considered likely.
Donald Trump's impeachment trial explained
With Chief Justice John Roberts presiding, Democrats argued on Thursday that Mr Trump’s motives were clear.
“No president has ever used his office to compel a foreign nation to help him cheat in our elections,” Rep. Jerrold Nadler of New York, the chairman of the House Judiciary Committee, told the senators. He said the nation’s founders would be shocked. “The president’s conduct is wrong. It is illegal. It is dangerous.”
They scoffed at Mr Trump’s claim he had good reasons for pressuring Ukraine to investigate his political foes.
It was Mr Trump who engaged in a shocking abuse of power, not former Vice President Biden or other Trump foes, said Representative Sylvia Garcia of Texas.
There was “no evidence, nothing, nada” to suggest Mr Biden did anything improper in dealings with Ukraine, said Ms Garcia, a former judge.
Mr Trump, with Mr Giuliani, pursued investigations of Mr Biden and his son, Hunter, who served on a Ukrainian gas company’s board, sought the investigation of debunked theories of what nation was guilty of interference in the 2016 US election.
The president’s defence waited its turn, which may come on Saturday.
“We will be putting on a vigorous defence of both fact and rebutting what they said,” said Trump lawyer Jay Sekulow.
Ahead of the day’s proceedings, Republican senator Roy Blunt said the Democrats were putting forward “admirable presentations” but added: “They’ve basically got about one hour of presentation, and they gave it six times on Tuesday and eight times yesterday. There’s just not much new here.”
The top Senate Democrat, Chuck Schumer, acknowledged that many senators “really don’t want to be here”.
But Mr Schumer said Mr Schiff had been outlining a compelling case about Mr Trump’s pressure on Ukraine and the scheme to cover up the charges, and that many Republicans were hearing it for only the first time.
He contended they could not but be “glued” to Mr Schiff’s testimony.
Once reluctant to take on impeachment during an election year, the Democrats are now marching toward a decision by the Senate that the American public also will judge.
Mr Trump blasted the proceedings in a Thursday morning tweet, declaring them the “Most unfair & corrupt hearing in Congressional history!”
Each side has up to three days to present its case.
After the House prosecutors finish, likely on Friday, the president’s lawyers will have as much as 24 hours.
It is unclear how much time they will actually take, but Mr Trump’s team promises not only to defend the president but to take apart the Democrats’ case.
The Senate is expected to take only Sunday off and push into next week.