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 Volodymr Zelensky.
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 Trump may have “crossed the Rubicon”.
Schiff, the influential head of the House Intelligence Committee, had previously opposed impeachment.
Hunter Biden served as director at a Ukrainian natural gas company while his father was Barack Obama’s vice-president with a significant role in US policy towards Ukraine.
Joe Biden is now the frontrunner to be the Democratic candidate who will take on Trump in the 2020 election.
The controversy over whether 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 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 the 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.
Trump told reporters on Sunday that the 25 July call 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 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 has quoted sources as saying Trump had urged Zelensky about eight times to work with his lawyer Rudy Giuliani on an investigation into Hunter Biden, but had not offered anything in return.
The Bidens deny any wrongdoing.
Democrats have been split on whether they should seek to impeach Trump over alleged wrongdoing.
However this latest story – which 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 Schiff, has thus far resisted demands for impeachment.