Photo: Mick Mulvaney, director of the Office of Management and Budget.
Former US Treasury Secretary Larry Summers pointed out the spending plan double-counts $2tr (£1tr).
But White House budget director Mick Mulvaney told reporters: "We stand by the numbers."
Unveiled on Tuesday, the budget proposes deep cuts to welfare programmes.
Mr Summers, also formerly chief economist of the World Bank, was one of the first to spot the apparent mistake. Image copyright Getty Images Image caption The budget proposal was unveiled during Mr Trump's first foreign trip as president
"It appears to be the most egregious accounting error in a presidential budget in the nearly 40 years I have been tracking them," he wrote on his blog.
He said the spending plan was "simply ludicrous".
The budget forecasts about $2tr in extra federal revenue growth over the next 10 years, which it uses to pay for Mr Trump's "biggest tax cut in history".
But that very same $2tr is then used to reduce the budget deficit.
"My observation is that there appears to be a logical error of the kind that would justify failing a student in an introductory economics course," Mr Summers wrote.
A prominent conservative economist agreed there was a discrepancy.
Douglas Holtz-Eakin, president of the American Action Forum and former director of the Congressional Budget Office, told the Los Angeles Times the numbers "don't seem to match"
That is not the only problem with President Trump's $4.1tr federal budget, according to analysts on both sides of the political divide.
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