The dollar index, already sliding, touched a low of 95.78, a decline of 0.6 percent, after the Reuters report. Treasury yields were also at the day's lows, and stocks lost some of their gains before finishing higher on the day. The 10-year yield was at 2.82 percent.
Trump has previously made it clear he does not like a strong dollar because it hurts U.S. exports. In the Reuters interview, he repeated claims that China artificially lowered its currency and that Europeans were manipulating the euro.
"This is about using the presidency as a bully pulpit," said Chandler. "This is like a red line for the market — the Fed's independence."
The president, who previously said he would not tell the Fed what to do, said he "should be given some help by the Fed." He also said he was "not thrilled with Powell."
In an interview with CNBC last month, Trump had called Powell a "good man" even while criticizing the Fed rate policy.
Market strategists say that Powell could act to show that the Fed is not being influenced by Trump's comments. The Fed is expected to raise rates in September, and Chandler said it may emphasize after that meeting that it could hike in December, just to make a point.
"I think people were looking for Powell to be more dovish [at Jackson Hole.] I didn't think he would be, but this precludes it," said Chandler. "I don't think there will be any new initiative or anything that would make it seem like he's acquiescing to the president."
Michael Schumacher, director, rate strategy at Wells Fargo, said he does not expect Powell to be influenced by Trump.
He's not the first president to complain about the Fed," he said. "Powell seems pretty comfortable brushing aside comments he doesn't want to address," he said.
"I think the market is assigning too much importance to his comments on the Fed. He can't impact it too much," Schumacher said.
Strategists said the comments on the yuan should not make much difference. Currency strategists have said China is lowering the fixing on its currency with the market, but it is not stopping the decline. Though it did set the currency higher Monday, as markets looked forward to talks between mid-level Chinese and U.S. officials this week.
"You can look at its currency and the currency started to move in a big way...It went wild in June. It seems to be coincident with the whole trade thing from the U.S. To me you can't say China's manipulating its currency," said Schumacher.