However, when asked if those allies were being used as a pawn as part of a bigger debate with other countries like China, Hassett said that wasn't the case.
"Nobody's being used as a pawn. I think that the president just wants reciprocal trade deals with all of our trading partners. And he is a person who knows how to negotiate," said Hassett, chairman of the White House Council of Economic Advisers.
"We've got to get people to the table," he told "Closing Bell."
He was elaborating on comments made during a press conference on Tuesday, when he touted Trump's negotiating skills.
"The president wrote the book, 'The Art of the Deal.' We're engaged in discussions and negotiations, and we're hopeful that we reach that positive long-run equilibrium," he told reporters Tuesday.
The recent tariffs on U.S. allies received a sharp response from G-7 finance ministers last weekend. They asked U.S. Treasury Secretary Steven Mnuchin to convey their "unanimous concern and disappointment" over the measures.
However, Hassett told CNBC the president's goal is to get everyone else to reduce their trade barriers to that of the U.S. That would increase the prosperity of America, as well as the rest of the world, he argued.
— Reuters contributed to this report.