According to the president, the Fed should cut interest rates "bigger and faster, and stop their ridiculous quantitative tightening NOW".
Markets had their worst day of the year on Monday after China allowed its currency to depreciate against the USA dollar, something that prompted the US government to angrily call Beijing a "currency manipulator".
Since its founding more than a century ago, the Federal Reserve has provided payment and settlement services, alongside and in cooperation with the private sector, as part of its core function of promoting an accessible, safe, and efficient US payment system.
America's central bank plans to build its own real-time payment system, much to the chagrin of big commercial banks.
Trump regularly points to the stock market as proof his policies are helping the economy, but, with Wall Street down as much as 500 points early Wednesday, he shifted gears.
Even as stocks and bond yields worldwide fell amid concern about Trump's escalating trade war with Beijing, he accused the United States central bank of being a bigger threat to the American economy than China.
The Fed is a private company backed by the US government. Trump has publicly said he could fire or demote Powell, his own nominee as chair.
And, despite the decision to lower rates, Trump was still displeased and renewed his attacks on the Fed and its chairman, Jerome Powell.
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"Collectively, we served our nation across almost 40 years and were appointed and reappointed by six presidents, both Republican and Democratic", the four former Fed leaders wrote, saying they had to make hard decisions to guide the economy.
The Board is now requesting comment on how the new service might be created to most effectively support the full set of payment system stakeholders and the functioning of the broader US payment system.
Volcker was first appointed by Democratic President Jimmy Carter and reappointed to a second term by Republican President Ronald Reagan.
But amid a lengthy economic recovery, the Fed has raised borrowing costs and winnowed bond holdings, measures that Trump has criticized.
"Our problem is not China", Trump wrote, pointing to alleged U.S. victories in the trade war with Beijing.
Federal Reserve Chair Jerome Powell cited the trade uncertainty as a factor in the decision to cut USA lending rates after four increases past year, amid worries about a slowing global economy.
"China dropped the price of their currency to an nearly a historic low". He also asked that the Fed ensure its new system be interoperable with the private banks' existing one. "It's called 'currency manipulation.' Are you listening Federal Reserve?"