"It's never stopped. No other President in history has had to put up with what I have had to", he wrote.
Mr Vance or the district attorney's office have not spoken about the grand jury proceedings, which are kept secret.
Mr Trump is also facing a separate criminal investigation from the New York Attorney-General's office. It also will hear other matters during that time, according to the Post.
The grand jury was set up recently and will sit three days a week for six months, reported The Washington Post, citing two unnamed people familiar with the case. He alleged that the probe "is purely political" and is "being driven by highly partisan Democrat prosecutors".
The Post reports the Manhattan DA is scrutinising whether the value of Trump Organisation properties were manipulated to defraud banks, insurance companies or tax authorities.More news: Blinken arrives in Israel to try to bolster Gaza ceasefire
The Trump Organisation did not respond to an AFP request for comment yesterday.
"After prosecutorial efforts the likes of which nobody has ever seen before, they failed to stop me in Washington, so they turned it over to NY to do their dirty work", Trump said in his statement, adding: "If these prosecutors focused on real issues, crime would be obliterated, and NY would be great and free again!" Next month's election is nearly certain to decide who it will be.
In February, the U.S. Supreme Court revealed how prosecutors would execute subpoenas at Trump's accounting firm to obtain eight-year tax statements and related documents from the former president, Trump organizations, and other Trump organizations.
Wrapping up his 12-year tenure then, Vance confirmed earlier this year that he will not seek reelection, and the grand jury's charging decision could be the last major development of his more than decade-long post.
Allen Weisserberg was summoned in a James civil investigation and witnessed twice past year.More news: Local Pharmacist Ready to Complete AstraZeneca Vaccinations More
Vence's research seems to have focused on Trump's longtime chief financial officer Allen Weisselberg in recent weeks. His former daughter-in-law, Jen Weisserberg, is cooperating with both inquiries.
Mr Trump has not been criminally charged.
Last week he attacked James and said he would "overcome" the indictment attempt.
She gave investigators a series of tax records and other documents when investigating whether some Trump employees were given off-book compensation such as apartment and school tuition.
This is a developing story.More news: COVID-19: downward trends continue as Alberta starts May long weekend