Trump's comments come amid a multitude of trade threats between major economies around the globe, after his initial tariffs on Chinese goods sparked a major conflict.
Mr Trump said increased rates had resulted in a stronger dollar which put the United States at a disadvantage compared with places where central banks are holding interest rates steady. The jump in the money supply "sends, I think, the wrong signal to the money markets", Reagan said in a 1982 press conference.
Hoping to keep a lid on inflation as the world's largest economy gathers pace, the Fed has raised its benchmark lending rate seven times since 2015 and expects two more rate hikes this year.
The chance inflation might accelerate has increased after the massive tax cut Trump championed, which has raised the USA debt and budget deficit.
The US, which is now doing well, should preserve its right to recover what was lost through such practices as illegal currency manipulation and trade deals that were not profitable for the US, the president tweeted.
The FTSE 100, which had edged up 11 points in early trading, fell almost 18 points to 7,666.00 after Donald Trump told CNBC's Joe Kernen in a Squawk Box interview today that he was prepared to tax all of the $505.5 billion of imports from China.
"We think the devaluation is on goal", Carl Weinberg, chief global economist at High Frequency Economics, wrote in a client note regarding China's latest currency change.
The White House in June already threatened to extend punishing USA duties progressively to up to $450 billion in Chinese imports.
The administration to date has slapped tariffs on $34 billion of Chinese goods in a trade dispute over what it calls the nation's predatory practices. The White House has also itemized $200 billion of additional Chinese imports that it said may be subject to tariffs.
Mr Powell, perhaps wary of provoking the ire of the president, has also been particularly careful in press conferences and congressional testimony when asked to comment on Mr Trump's tax and trade policies.
It turns out President Bill Clinton didn't want to speak about the Fed's decisions as a tactic to avoid looking vulnerable. President Xi Jingping "cannot lose face with his own people by giving in to the United States", Dollar said. "But it was very unfair".
Analysts say they're becoming more convinced that Trump's multi-front trade fights aren't merely a short-term negotiating ploy.
The growing share of worldwide trade under threat has raised the prospect the escalating trade war could harm the global economy by disrupting companies supply chains, pushing firms to hold off on investments, and making goods more expensive for consumers.
Mr Trump has said before that he favours low interest rates, and dismissed concerns about his interference.
"There's no negotiating going on that I can see", Dollar said.
"We've been ripped off by China for a long time", he added.
The Chinese yuan hit its lowest level in over a year on Friday, as its central bank indicated it was willing to tolerate a weaker currency.