It’s hard to know where to begin in describing the gross impropriety of Mr. Trump’s behavior. But we’ll start with facts: The allegations that the president is suggesting Ukraine and China should investigate are manifestly false. Abundant evidence disproves the charge that Mr. Biden, as vice president, sought the dismissal of a Ukrainian prosecutor to protect his son Hunter, who was then on the board of a Ukrainian gas company. And Mr. Trump’s claim that Hunter Biden took “billions of dollars” out of China is even more ludicrous. Hunter Biden joined the advisory board of an investment fund with Chinese partners, but, his lawyer said, has earned no return or compensation.

Mr. Trump is seeking to call attention to Hunter Biden’s business involvement with foreign partners who were probably hoping to trade on his family name. That’s unseemly — but no more so than the business favors obtained by Mr. Trump’s own children from China and other countries. If there were actual evidence of wrongdoing in these relationships, it should be investigated not by foreign authorities but by the Justice Department, which could properly ask other governments for cooperation, if any were needed.

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That a request for a foreign investigation of a U.S. citizen would come directly from the president, in the absence of any legitimate U.S. probe, is a blatant violation of that citizen’s rights and of the U.S. rule of law. That Mr. Trump does it in front of television cameras makes it no less egregious: In doing so, he is attempting to normalize what should be utterly unacceptable presidential behavior.

Historian Robert Kagan recently described in The Post what the consequences would be if Mr. Trump’s actions went unpunished. “Sending the signal that other governments can curry favor with a U.S. president by helping to dig up dirt on his or her political opponents would open our political system and foreign policy to intervention and manipulation on a global scale,” he wrote. “Every government in the world wishing to influence U.S. foreign policy will have an incentive to come to a sitting president with information on his or her potential political opponents.”

Mr. Trump is in the midst of trade negotiations with the Chinese regime of Xi Jinping and has at times conversed directly with Mr. Xi about the terms of a deal. Will he raise his request for an investigation of Mr. Biden when he next bargains with the Chinese ruler? “That’s something we can start thinking about,” Mr. Trump said Thursday. Mr. Trump sees nothing wrong with making such requests. What about congressional Republicans? Do they really wish to see such use of the president’s office become the new normal of American politics?