As part of a criminal investigation by the office of Manhattan District Attorney Cyrus Vance, a Democrat, subpoenas were issued to Mazars for financial records including almost a decade of Trump's tax returns to be turned over to a grand jury in New York City.
Manhattan prosecutors are seeking the tax returns as part of a probe that includes hush-money payments to women who claim they had affairs with Trump.
Lower courts in Washington and NY ruled against the president in all cases, but those decisions have been put on hold pending a final court ruling.
The tax returns case also is headed back to a lower court, but Trump's major arguments have now been rejected.
"We are overjoyed that, once again, the Supreme Court has protected our right to serve the elderly without violating our faith", said Mother Loraine Marie Maguire of the Little Sisters.
House committees issued subpoenas seeking Trump's financial records from his longtime accounting firm Mazars LLP and two banks, Deutsche Bank and Capital One.
The subpoenas - orders to hand over evidence - were issued a year ago to Mazars USA, who are Mr Trump's accountants, and to major Trump lenders Deutsche Bank and Capital One. The case is scheduled to be argued in the court term that begins in October.
"Congressional and criminal investigators must continue working to ensure that the public gets answers to the questions Trump refuses to give about his finances", said Quint and Eldridge.
In the birth control case, two liberal justices who sided with the administration, Elena Kagan and Stephen Breyer, nonetheless suggested the legal fight over the Trump administration changes may not be over.
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Mr Trump has predicted a " fireworks display like few people have seen" in South Dakota , a state he won in the 2016 USA election. Event organizers were to provide masks to anyone who wanted them and planned to screen attendees for symptoms of COVID-19.
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The tax returns would not be made public since they would be released to a grand jury, which is secret.
However, if the NY grand jury indicts the president and Vance files charges against him before the November election, the contents of his financial records could become public through that process.
Judges appointed by Mr Nixon and Mr Clinton voted against them in the cases.
"The court's decision threatens to impair the functioning of the presidency and provides no real protection against the use of the subpoena power by the nation's 2,300+ local prosecutors", Alito wrote. A federal appellate court came to a similar conclusion in a separate case concerning the House's subpoena of former White House counsel Don McGahn.
The House Financial Services, Intelligence and Government Oversight committees said the subpoenas were in the exercise of their oversight and legislative responsibilities.
Trump blasted the decision, insisting that courts in the past had deferred to presidents in such matters.
The decisions were in line with earlier Supreme Court cases involving presidential accountability.
Trump, for his part, vociferously defended himself Thursday. Trump said the House should have to show that the records are "demonstrably critical" to a legislative objective, an approach Roberts said "would risk seriously impeding Congress in carrying out its responsibilities". He did not rule out the possibility that the House subpoenas could be enforced in the future, but delayed, for now, the prospect that the documents will be turned over to Democrats before the November election.