As Hurricane Michael pounded the Southeast on Wednesday, Trump took shelter at the campaign rally in Pennsylvania, where he sought to boost Republicans before the midterms.
At IMF meetings in Bali, Lagarde said she "would not associate" Fed chair Jerome Powell "with craziness".
Mnuchin met People's Bank of China Governor Yi Gang on Friday, but did not attribute the currency comments directly to him.
Trump said Tuesday that the economy is enjoying "record-setting" numbers and "I don't want to slow it down even a little bit, especially when we don't have the problem of inflation".
Trump's blunt public criticism of the Fed, which began this summer, is without precedent.
Earlier in the day, Trump told the Fox & Friends television broadcast that the central bank was "making a big mistake" by being "too aggressive" in raising rates. This could be a worry for Fed officials trying to keep a lid on inflation.
United States presidents have rarely criticised the Fed in recent decades because its independence has been seen as important for economic stability.
From its beginning, the Fed was created to insulate it from political pressures. But the larger question than how the Fed actions are affecting Trump politically is should this private monopoly have this kind of power over interest rates in the first place?
There are multiple ways that the Federal Reserve can manipulate the economy through interest rates. Over the past year, the Fed has been raising rates once every quarter, or a pace of four times in a year. "The problem in my opinion is Treasuries and the Fed". That gave Carter an opening to make Paul Volcker the new Fed chairman, someone the Carter administration regarded as better equipped to combat high inflation. One is that higher rates make it more expensive to borrow, which can tap the brakes on economic growth. Under President Trump, the Dow was up 33% as of last week. But Bush's complaint about the Fed came years after he had left office. Increased borrowing demand by Uncle Sam would lead to rising rates, all things being equal.
The Fed has increased the cost of housing, the cost of investing, and the cost of tuition by hiking rates.
The precipitous fall of the market in previous days has alarmed Trump who had tethered his electoral fortunes to soaring stocks.
"We know the Fed is independent".
The median forecast of FOMC officials in September called for interest rate increases to continue into 2020, rising from 3.1% at the end of 2019 to 3.4% at the end of 2020.
Trump said he had no intention of firing Powell.
"The Fed has an independence that it needs to pursue, it's concerned about inflation - and right now we have tariffs, which are wreaking havoc, we're not sure to what extent, and an exploding deficit ..." "The Fed is going loco and there's no reason for them to do it".
Fed spokeswoman Michelle Smith declined to comment on Trump's remarks. Rather, he has stressed that the central bank handles its job without regard to politics. When interest rates rise, bond yields typically do as well as investors pull money out of stocks and move them into bonds to capitalize on the higher (and safer) returns. "I expressed my concerns about the weakness of the currency". He didn't say anything remotely like that, ' he said on CNBC.