US President Donald Trump lashed out at Democrat Joe Biden on Sunday, strongly suggesting on Twitter that he and his family were corrupt and saying the former vice president should "hang it up."

In a series of Twitter posts, the president advanced widely discredited allegations that Biden interfered improperly to protect his son Hunter from suggestions of corrupt dealings in Ukraine, and that the younger Biden also made USD 1.5 billion in a questionable deal in China.

"Based on all of the money he and his family probably 'extorted,' Joe should hang it up," Trump said.

The roiling scandal prompted the Democratic-controlled House last month to open an impeachment inquiry into Trump's efforts to pressure Ukraine to investigate the Bidens.

Trump's tweets followed the former vice president's strongest response yet to the situation -- one that has left Biden struggling to regain the momentum that for months has had him leading the Democratic pack seeking the 2020 presidential nomination.

In an op-ed article in The Washington Post, Biden said Trump was "frantically pushing flat-out lies, debunked conspiracy theories and smears against me and my family, no doubt hoping to undermine my candidacy."

"It won't work, because the American people know me -- and they know him," Biden wrote.

"I will put the integrity of my whole career in public service to this nation up against Trump's lack of integrity any day."

Trump tweeted on Sunday that he would "LOVE" running against Biden, before adding, "I just don't think it's going to happen." But Biden concluded his op-ed with these words for Trump: "Please know that I'm not going anywhere. You won't destroy me, and you won't destroy my family. And come November 2020, I intend to beat you like a drum."