The United States will not rule out tariffs on China as a "negotiating" or "enforcement" tool, despite "progress" made last week during talks with Beijing, Larry Kudlow, President Donald Trump's top economic advisor, said Monday.

On Sunday, Treasury Secretary Steven Mnuchin said the world's two largest economies "are putting the trade war on hold" as they try to cement and implement the framework of an agreement addressing trade imbalances. The potential deal would involve China lowering its trade barriers and the U.S. exporting more goods such as agricultural and energy commodities.

In tweets Monday morning, Trump said China "has agreed to buy massive amounts of ADDITIONAL Farm/Agricultural Products." He separately wrote that barriers and tariffs would "come down" for the "first time."

Trump tweet: China has agreed to buy massive amounts of ADDITIONAL Farm/Agricultural Products - would be one of the best things to happen to our farmers in many years!

Trump tweet: On China, Barriers and Tariffs to come down for first time.

The tentative deal — the specific details of which remain unclear — would reduce trade tensions and avoid tariffs that threatened to damage the world's two largest economies. However, Kudlow stressed Monday that the U.S. would not take tariffs off the table entirely amid ongoing negotiations.

"Tariffs are suspended right now, as per Mr. Mnuchin. That's a good thing," the director of the National Economic Council told CNBC's "Squawk on the Street." "But you cannot remove tariffs as a negotiating tool or an enforcement tool from this process. You cannot do that. And therefore, I don't think we're saying tariffs are over. Far from it."