The President-elect had promised to clear up the situation before electors meet to approve his candidacy on 19 December, scheduling a press conference for this Thursday.
But on Tuesday evening, Mr Trump announced that he would be delaying any decisions until January - meaning members of the Electoral College will be expected to vote him in despite the real danger he could violate the US Constitution from the moment he is inaugurated.
Mr Trump’s various overseas business interests, as they stand, are almost certainly in breach of the Emoluments clause of the Constitution - stating that no elected official may take payment or profit in any kind from a foreign leader or state.
His domestic businesses, particularly the public lease on the new Trump International Hotel in Washington, will also throw up conflicts of interest when he becomes president.
Ethicists have said the only satisfactory way Mr Trump could assuage these conflicts is to hand his entire business empire over to a blind trust, as other presidents have done before him.
But in a series of tweets on Tuesday night, in which he said he would “hold a press conference in the near future” to provide more detail, Mr Trump said he would hand control of his businesses over to his adult sons - a measure which would not remove the appearance of a conflict.
He also said he would be simply "leaving" his businesses rather than fully divesting, and added there would be "no new deals will be done during my term(s) in office".
Former White House ethics lawyers Richard Painter, who served under George W Bush, and Norman Eisen, who served under Barack Obama, have issued a joint statement explaining why that’s so problematic.
They said: “With Trump's cancellation of his announcement of how he will handle his admitted business conflicts, electors are now confronted with voting for a man who will be in violation of the Constitution on day one unless he divests, and who has not told us his plan to do that.
“As we have previously said, electors should search their consciences. Now they must search twice as hard.”
One Republican elector has already pledged not to vote for Mr Trump on the basis that he is unqualified to lead, meaning 36 more would need to join him in under a week if there were to be any chance of the Electoral College blocking the election result.
But the conflicts in particular represent a difficult situation for the College which, according to founding father Alexander Hamilton, was set up to ensure “that the office of President will never fall to the lot of any man who is not in an eminent degree endowed with the requisite qualifications”.
Eisen told Quartz: “He is hesitating in response to an outcry including last week’s bipartisan letter, and to the fact that two thirds of Americans are concerned about his conflicts. This is the latest in a series of backtracks by the President-elect.
“Let’s hope he takes the additional time to do the right thing, follow every president for the past four decades, and divest into a blind trust or the equivalent.”
Mr Trump’s assertion in his tweets that he is “not mandated by law” to give up control of his businesses is debatable at best, as ethicists have previously documented. In short, being the President will shield him from some aspects of conflict-of-interest laws - but by no means all of them.
His activities since becoming President-elect suggest he holds little regard for the public appearance of conflicts. This week we learned he will not even give up his role as executive producer on the Celebrity Apprentice, despite the fact that the company which makes it relies on government permits to build its casinos.
He considered making his son-in-law Jared Kushner a White House advisor, and then a Middle East envoy, despite clear anti-nepotism laws.
And he allowed his daughter Ivanka Trump - an executive in his business empire - to sit in on a meeting with the Japanese Prime Minister.
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