Hassett told an NBC News reporter at the White House that Powell's role as the leader of the U.S. central bank is "100 percent" safe.
That assurance followed Hassett's appearance on Fox Business, where the head of Trump's Council of Economic Advisers said he is highly confident that the president is happy with Mnuchin.
Hassett has made multiple public appearances in recent days, attempting to assuage markets amid growing concerns about Trump's reported displeasure with Mnuchin, who has served in the president's Cabinet since February 2017, and Powell, who oversaw a hike in interest rates last week.
Before that quarter-point rate rise, Trump had complained in a tweet that it was "incredible" for the Fed to consider "yet another interest rate hike." Presidents traditionally do not comment publicly on actions taken by the Fed, which is considered independent from the White House.
Multiple outlets reported Saturday that Trump had vented his frustrations about Powell and had privately expressed a desire to fire him.
Mnuchin attempted to brush those reports aside in a pair of tweets Saturday, quoting Trump as saying he "never suggested" firing Powell.
On Monday, Trump lashed out at the central bank again in a tweet, saying, "The only problem our economy has is the Fed."
The news appeared to accelerate equities' decline Monday, marking the stock market's worst Christmas Eve performance on record.
CNN, citing a source close to the White House, reported Wednesday morning that Mnuchin's job could be in "serious jeopardy."
Trump, however, said on Christmas Day that he had confidence in Mnuchin, telling reporters that Mnuchin is a "very talented, very smart person."
Over the weekend, Mnuchin spoke with the heads of the six largest U.S. banks, and tweeted a statement afterward assuring that none of them have "experienced any clearance or margin issues."
As markets struggled to gain a foothold Wednesday morning, the partial shutdown of the federal government entered its fifth day, with no immediate end in sight.
But Hassett told NBC that even a "few-week shutdown is not going to be something that has any kind of significant effect on the outlook" of the economy.
Asked whether Trump is continuing to blame the Fed for the volatility in the markets, Hassett said his job is to "respect the independence of the Fed and not comment on monetary policy."