USA automakers, dealers and suppliers remained united in opposition to the president's tariffs for fear it would drive prices up.
The US economy has so far proven resilient to Mr Trump's threat of taking a trade conflict to the next level.
On Friday, the Axios news website reported that Kudlow had said Trump was "not going to let go" of the trade issue. "We have been ripped off by China for a long time", he said.
The U.S. imported $505 billion in Chinese goods in 2017, while China imported $130 billion in American products, according to the Commerce Department.
Trump has also targeted steel and aluminum exports from the EU and has threatened to tax European cars sold on the American market.
The dollar index .DXY , a measure of its value against a basket of six major currencies, was on track to post its largest one-day loss in three weeks.
The dollar weakened the most since March, Treasuries tumbled, and stocks closed mostly lower Friday after President Trump's verbal salvos fanned investor concern that a global trade war is escalating.
Trump, however, has made reducing US trade deficits a priority and the combination of rising interest rates and a strengthening dollar pose risks for export growth. On Thursday, automakers and vehicle-making nations such as Mexico criticized the administration's study into whether auto imports pose a risk to national security, which could lead to tariffs.More news: Amid uproar, Trump says he’s ‘looking forward’ to second meeting with Putin
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He said the Fed's course of tightening monetary policy "now hurts all that we have done".
He also said that higher interest rates will strengthen the USA dollar too much, putting the United States at a "disadvantage" while central banks in Europe and Japan keep rates low.
I put a very good man in the Fed. Chinese Commerce Ministry spokesman Gao Feng last week called those accusations "groundless" and said that the US trade penalties contravene rules at the World Trade Organization.
In an interview with CNBC, Trump said he was "not thrilled" that the Fed was raising rates and thus causing upward pressure on the dollar.
Many companies in the USA are opposed to the administration's use of tariffs against China, saying they risk hurting business and the economy without being likely to change behaviour.
"We're looking at 4.0 percent GDP growth for Q2, record low unemployment, the lowest initial jobless claims number in 50 years, and inflation above the official target", he said. "Debt coming due & we are raising rates - Really?" he tweeted.
The Fed raised interest rates twice this year and Mr. Powell said two more increases are likely before the end of 2018.
The central bank's job is to keep prices stable, including raising interest rates to prevent the economy from overheating and inflation from rising.