President Trump has confirmed that he raised the subject of former Vice-President Joe Biden and his son in a July phone call with Ukrainian president Volodymyr Zelensky.
Mr Trump is facing allegations that he pressured Ukraine to investigate his potential 2020 rival, which he denies.
But his admission about the phone call fuelled calls for Democrats to launch impeachment proceedings in Congress.
Adam Schiff, a senior Democrat, said Mr Trump may have “crossed the Rubicon”.
Mr Schiff, the influential head of the House Intelligence Committee, had previously opposed impeachment.
What’s the background?
Hunter Biden became a director at Ukrainian natural gas company Burisma in 2014 while his father was Barack Obama’s vice-president with a key role in US policy towards Ukraine.
Joe Biden is now the frontrunner to be the Democratic candidate who will take on Mr Trump in the 2020 election.
The controversy over whether Mr Trump pushed his Ukrainian counterpart to launch corruption investigations against the Bidens has dominated Washington in recent days.
It was sparked after revelations in US media that an intelligence whistleblower had filed a complaint over Mr Trump’s communications with a foreign leader and a “promise” that was allegedly made.
It emerged last week that the Trump administration was blocking the whistleblower complaint from being handed over to Congress, despite the intelligence inspector general judging it to be “urgent”.
Under US law, if a complaint is considered to be of “urgent concern”, and if the inspector general considers the complaint to be “credible”, then the department head is expected to share the information with Congress within seven days.
What did Trump admit?
Mr Trump told reporters on Sunday that the 25 July call with Mr Zelensky was “congratulatory”, but mentioned corruption and “largely the fact that we don’t want our people, like Vice-President Biden and his son, creating to the corruption already in the Ukraine”.
But he insisted he had done “absolutely nothing wrong”. He has previously accused the whistleblower of being “partisan” and said he knew all his phone calls to foreign leaders were listened to by US agencies.
While Mr Trump suggested a transcript could be released, senior Trump administration officials said it would be inappropriate for private conversations between world leaders to be made public.
The Wall Street Journal (WSJ) has quoted sources as saying Mr Trump had urged Mr Zelensky about eight times to work with his lawyer Rudy Giuliani on an investigation into Hunter Biden, but had not offered anything in return.
Why President Zelensky is using the ‘ostrich defence’
By Jonah Fisher, BBC News, Kiev
So far, President Zelensky and his team have taken the head-in-the-sand approach to this crisis.
There has been no transcript of the 25 July call, and no confirmation of the WSJ story that Ukraine’s president was asked eight times to investigate the Bidens.
The comedian-turned-president is acutely aware of the dangers of being sucked into US electoral politics, of being seen to take sides in what could well be a Trump-Biden election campaign this time next year.
Whether the “ostrich defence” can survive a meeting in New York with President Trump on Wednesday remains to be seen.
If not a full investigation, the US president and his advisers will almost certainly be looking for some acceptance from Ukraine’s leader that the Biden story is more than a fabricated conspiracy.
Even a brief word from Mr Zelensky that he would “look into” the Bidens would allow the White House to keep the focus on the former vice-president and his son’s activities, rather than the now infamous phone call.
What is the Biden story?
When Hunter Biden joined Burisma in 2014, questions were raised about a potential conflict of interest for his father. Ukraine was undergoing a political transition after its pro-Russia president was forced out of office, and the elder Biden was making frequent trips to the country.
In 2016, Mr Biden pushed the Ukrainian government to fire its top prosecutor, Viktor Shokin, whose office had been investigating the oligarch owner of Burisma.
In a speech last year at a think-tank he boasted of having used a billion-dollar loan guarantee to successfully force Mr Shokin out.
“I looked at them and said ‘I’m leaving in six hours: if the prosecutor is not fired, you’re not getting the money’,” he said.
Mr Trump and his allies accuse Mr Biden of having acted to protect his son. However, several western governments and major financers of Ukraine’s government also wanted Mr Shokin dismissed because he was seen as a barrier to anti-corruption efforts.
Mr Shokin had also shown little appetite for pursuing Burisma.
Joe Biden has said he has never spoken to his son about his business dealings.
What’s being said about impeachment?
Democrats have been split on whether they should seek to impeach Mr Trump over alleged wrongdoing.
However this latest story – which Mr Trump’s opponents allege could amount to inviting foreign interference in the 2020 election – appears to have pushed some senior Democrats closer to backing such a move.
House Speaker Nancy Pelosi said that if the whistleblower complaint was not turned over to Congress the Trump administration would “be entering a grave new chapter of lawlessness which will take us into a whole new stage of investigation”.
Ms Pelosi, like Mr Schiff, has thus far resisted demands for impeachment.