Washington had strongly signaled to Sullivan that he should allow this unusual appeal — ruling that Sullivan had probably “abused his discretion” when he denied an earlier attempt.

In his ruling, Sullivan noted that this sort of appeal — done in the middle of a district court case instead of at its end — is warranted when there is “substantial ground for difference of opinion” on a key matter of law. The appeals court had indicated that this was such a case, so he agreed to let the appeal go forward.

One effect of Sullivan’s ruling will be to keep on hold the “discovery” process, a pretrial fact-finding period in which the Democrats wanted to serve 37 subpoenas on Trump businesses, asking about their foreign customers.

Sullivan had paused that process in July after the appeals court’s ruling.

Earlier, attorneys working with the Democrats said that subpoenas delayed would, in effect, be subpoenas denied — that Trump’s first term might run out before the plaintiffs could get any answers. They also questioned Trump’s lawyers’ argument that the suit was a distraction.

“There is simply no reason — and the President has offered none — why discovery against businesses that he plays no role in running should ‘distract [him] from the performance of his constitutional duties,’ ” the lawyers wrote in recent court filings, trying to persuade Sullivan to let discovery continue.

Sullivan rejected that argument.

The decision is another setback for those who hoped to use the courts — and the Constitution’s emoluments clauses — to stop Trump’s private business from taking money from foreign governments.

Those clauses — intended to prevent U.S. leaders from being corrupted through their wallets — prohibit presidents from taking payments from foreign states, U.S. states or the federal government. Until Trump’s presidency, they were seen as dusty footnotes from another era.

But then Trump chose to keep ownership of his private businesses, including a D.C. hotel that has hosted embassy galas and visiting foreign leaders.

Three plaintiffs filed suit — seeking to prohibit Trump from doing business with foreign countries, or at least require him to give details about who paid what.

So far, his businesses have not done either.

Two of the cases have been dismissed, as courts ruled that those plaintiffs — a nonprofit watchdog group in one case, and the attorneys general of the District and Maryland in the other — did not have the legal right to sue Trump.

The attorneys general have said that they are considering asking for a rehearing of the case and that they expect the issue eventually to reach the Supreme Court.

In this case, the U.S. Court of Appeals for the D.C. Circuit appears keenly interested in hearing the Democrats’ case, which will involve the appeals’ judges considering a novel legal question: Who has the standing to sue Trump over the emoluments clauses?

The Justice Department, representing Trump, has said that individual legislators do not have the authority to seek this kind of help from the courts. A Justice Department spokesperson did not immediately respond to a request for comment.

Two of the lead plaintiffs — Sen. Richard Blumenthal (D-Conn.) and Rep. Jerrold Nadler (D-N.Y.) — said that they “look forward” to the appeal. “Every day that goes by is another day that President Trump violates the Constitution,” the two said in a statement.

Carol D. Leonnig contributed to this report.