Later Wednesday, White House press secretary Sarah Huckabee Sanders said the administration expects China to "make changes and stop the unfair trade practices." If Beijing does not make changes, she believes the White House will move forward with the tariffs.
In any case, Sanders said it would take "a couple months" for tariffs to get implemented following a review process.
On Tuesday, the Trump administration unveiled a list of Chinese imports it wants to target in retaliation for alleged intellectual property theft. The proposed measures, which companies will have a chance to comment on, seek to target about $50 billion worth of Chinese products every year.
China then announced tariffs on 106 American products such as soybeans, cars and whiskey. The administration does not expect to take any more trade action to react to China this week, according to a White House official who declined to be named.
The moves were the latest escalation of trade tensions between the world's two largest economies. Fears of a trade war led to major U.S. stock indexes diving on Wednesday morning, only to make up some of those losses throughout the day.
Kudlow called the stock market reaction to the moves "mild" and cautioned against overreacting to the moves. He contended the U.S. would not lose in a trade war with China.
Kudlow, a free-market advocate and longtime CNBC personality, started in his White House position this week.
— CNBC's Eamon Javers and Kayla Tausche contributed to this report