WASHINGTON – Already under investigation for asking Ukraine to dig up dirt on Joe Biden, an unrepentant President Donald Trump said Thursday that China should also investigate his political foe – an all-but-engraved invitation to another foreign country to inject itself into U.S. politics.

"By the way, likewise, China should start an investigation into the Bidens because what happened in China is just about as bad as what happened with Ukraine," Trump told reporters.

Democrats and other critics denounced Trump for invoking China, saying he wants yet another country to interfere in the next U.S. presidential election just as Russia did in 2016.

"The defining characteristic of Donald Trump's presidency is the ongoing abuse of power," said Biden spokeswoman Kate Bedingfield. "The White House itself has admitted that Donald Trump tried to bully a foreign country into lying about the domestic opponent he's afraid to look in the eye next November."

Speaking with reporters en route to Florida for a Medicare speech, Trump also acknowledged that he did indeed want Kiev to investigate Biden and his son, though he denied using foreign aid as leverage.

Asked if he had requested President Xi Jinping of China to help investigate the Biden family, Trump said, "I haven't but it is certainly something we could start thinking about."

Some critics noted that Trump's call for China to investigate Biden came less than a week before American and Chinese negotiators meet to try and revive a proposed bilateral trade agreement. The Trump administration has been engaged in a longstanding trade war with Beijing.

"It is the president saying to a foreign government that it will win his favor by investigating the Bidens," said David Rothkopf, a foreign policy analyst and critic of Trump. "And he is saying it in the middle of a massively important trade negotiation so the stakes could not be higher for China."

In firing back at Trump, Biden's campaign compared the president's remarks to his open-ended call in 2016 for Russia to "find" Democrat Hillary Clinton's emails.

Trump "is flailing and melting down on national television, desperately clutching for conspiracy theories that have been debunked and dismissed by independent, credible news organizations," Bedingfield said.

Biden, the vice president under Obama, has said that Trump is targeting him because he fears defeat in the next election.

"He is repeatedly smearing me and my family," Biden said Wednesday. "His party fans out to carry the smear. Millions of dollars in dishonest attack ads are blanketing the airwaves – paid for by the special interests so well served by his presidency."

Current Vice President Mike Pence, who has kept a low profile in recent days, expressed support for Trump's actions. “The American people have the right to know whether or not the vice president of the United States or his family profited from his position,” Pence told reporters during a stop in Scottsdale, Arizona.

Pence later tweeted out a wire story about his comments.

House Speaker Nancy Pelosi, D-Cal., who authorized the impeachment inquiry last week, referenced Trump's comments in responding to a request by House Republican leader Kevin McCarthy, R-Calif., to suspend the investigation.

In rejecting that suggestion, Pelosi replied to McCarthy that "I received your letter this morning shortly after the world witnessed President Trump on national television asking yet another foreign power to interfere in the upcoming 2020 elections."

At the heart of Congress' probe into the president's actions is his claim that Biden strong-armed the Ukrainian government to fire its top prosecutor in order to thwart an investigation into a company tied to his son, Hunter Biden. But sources ranging from former Obama administration officials to an anti-corruption advocate in Ukraine say the official, Viktor Shokin, was ousted for the opposite reason Trump and his allies claim.

One of Trump's contentions is that Hunter Biden landed business opportunities in Ukraine and China because of his connection to Joe Biden, and that the senior Biden used his position to protect his son.

There is no evidence of any improper activity by either Biden.

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Before leaving the White House, Trump wrote at least 20 tweets and re-tweets, many of them attacking the ongoing impeachment inquiry into his dealings with Ukraine.

Trump also turned to immigration, dismissing a series of reports that he has floated ideas of harming migrants to dissuade them from attempting to enter the U.S. Specifically, Trump denied a New York Times report that the president had previously asked about shooting migrants in the legs to slow them down.

"Fake News, just like the snakes and gators in the moat," Trump said, referring to another report that he had inquired about using alligators to discourage migrants. "The Media is deranged, they have lost their minds!"

A USA TODAY/Ipsos Poll released Thursday found that Americans by a 45%-38% plurality support a House vote to impeach Trump.

Contributing: Courtney Subramanian