His comments came after a federal judge’s ruling that granted Manhattan’s top prosecutor access to his tax returns.
US District Judge Victor Marrero’s ruling echoed his prior decision in the case, upheld last month by the US Supreme Court.
The high court had returned the case to Judge Marrero’s courtroom to give Mr Trump’s lawyers a chance to raise other concerns about the subpoena issued by Manhattan District Attorney Cyrus Vance Jr.
Mr Vance has been seeking Mr Trump’s tax returns from the president’s longtime accounting firm, Mazars USA, for more than a year, since Mr Trump’s former personal lawyer Michael Cohen told Congress that the president had misled tax officials, insurers and business associates about the value of his assets.
Congress is also pursuing Mr Trump’s financial records.
Mr Trump’s lawyers immediately appealed over Judge Marrero’s Thursday ruling to the Second Circuit Court of Appeals.
The president said he expected the case to end up back before the Supreme Court.
The appeal means it is unlikely Mr Vance’s office will get its hands on Mr Trump’s tax returns before November’s presidential election.
Because they are being sought as part of a confidential grand jury investigation, they would not automatically be made public.
“The Supreme Court said it’s a fishing expedition. You don’t have to do it,” Mr Trump said.
“And this is a fishing expedition, but more importantly, this is a continuation of the witch hunt – the greatest witch hunt in history. There’s never been anything like it, where people want to examine everything you’ve ever done to see if they can find that there’s a comma out of place.”
Mr Trump is the only president in modern times who has refused to make his tax returns public.
Before he was elected he had promised to release them.
Mr Trump’s lawyers have said that the request for tax records dating back to 2011 was retaliatory after the president’s company, the Trump Organisation, disputed the scope of a subpoena seeking records from June 1 2015 until September 20 2018.
We’re not doing things wrong, but they’ll say, ‘Let’s go in and inspect every deal he’s ever done'
That time span pertains to an investigation related to payoffs to two women – porn actress Stormy Daniels and model Karen McDougal – to keep them quiet during the 2016 presidential campaign about alleged extramarital affairs with Mr Trump.
The president has denied the affairs.
Mr Trump, through his lawyers, has argued that the subpoena was issued in bad faith, might have been politically motivated and amounted to harassment of him, especially since the wording mimicked the language in congressional subpoenas.
Mr Vance’s lawyers said they were entitled to extensive records to aid a “complex financial investigation” and they cited in their papers public reports of “extensive and protracted criminal conduct at the Trump Organisation”.
In July, the Supreme Court rejected Mr Trump’s arguments that he cannot even be investigated, let alone charged with any crime, while he is in office.
But the court left open the prospect that Mr Trump could make new arguments in a bid to keep the subpoena from being enforced.
Also in July, the Supreme Court kept a hold on banking and other documents about Mr Trump, family members and his businesses that Congress has been seeking for more than a year and returned the case to a lower court.
Mr Trump, in reacting to Thursday’s developments, boasted about previous legal victories – including in special counsel Robert Mueller’s investigation of Russian election interference – as he doubled down on his contention that there was a concerted effort to make him look bad.
“We’re not doing things wrong, but they’ll say, ‘Let’s go in and inspect every deal he’s ever done’,” Mr Trump said.
“‘Let’s get papers from 10 years, every paper, every deal he’s ever signed, maybe we can find where some lawyer made a mistake, where they didn’t dot an i, where they didn’t put a comma down someplace, and then we can do something’.”