Monday’s court filing suggests the investigation is broader than claimed bribery money payments given to two women who claim they had affairs with Trump.
The Supreme Court ruled last month that attorneys could inspect the tax returns.
President Donald Trump has allegedly banned the investigation, calling it a “witch hunt”.
Manhattan District Attorney Cyrus Vance Jr has opened a subpoena to acquire eight years of Trump’s personal and corporate tax returns, which the Trump Organization is challenging.
The Republican president blames the Manhattan prosecutor, a Democrat, of following a political feud.
Last week, President Donald Trump’s lawyers opened a complaint quarreling the warrant was “wildly overbroad” and given in bad faith.
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Responding in court documents filed on Monday, lawyers for Mr Vance said that accusations of criminal activity at the Trump Organization date back “over a decade”.
His lawyers commended newspaper articles about alleged bank and insurance fraud at the Trump Organization and congressional testimony by the president’s former lawyer Michael Cohen, who said Mr Trump would belittle his assets when trying to reduce his taxes.
They said their investigation extends beyond claimed bribery money payments made to adult film star Stormy Daniels and former Playboy model Karen McDougal in the lead-up to the 2016 election.
Such payments could result to violate campaign financing laws. The president disagreed that the affairs happened.
Speaking to reporters, Mr Trump described the investigation as “Democratic stuff”.
“They failed with Mueller,” he said, referring to the justice department investigation by special counsel Robert Mueller that failed to establish the president had colluded with the Kremlin during his election campaign. “They failed with everything, they failed with Congress, they failed at every stage of the game.”
He added: “This is a continuation of the worst witch hunt in American history.”
President Donald Trump who inherited money from his father and went on to become a property developer, is the first president since Richard Nixon not to have made his tax returns public while running for office.
The Manhattan district lawyer has himself come under inspection.
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In 2012 Cyrus Vance allegedly dropped a potential fraud inquiry into Ivanka Trump and her brother, Donald Trump Jr, for supposedly misrepresenting the value of apartments to prospective buyers.
According to US media, Mr Vance got rid of the inquiry following a visit from Marc Kasowitz, a attorney for the Trump siblings’ father. Mr Kasowitz later raised more than $50,000 for Mr Vance’s re-election campaign.
Questions have also been required as to why Mr Vance did not bring charges against Harvey Weinstein back in 2015 relating to an Italian model’s accusation that the Hollywood producer had fondled her.
Two lawyers for Weinstein, who was sentenced this year of sex offences, were also donors to Mr Vance’s election campaign, as stated by the New Yorker.
The publication said prosecutors within Mr Vance’s own office had described him as publicity hungry.
