Commerce Secretary Wilbur Ross told CNBC on Wednesday that President Donald Trump has indicated a degree of flexibility on tariffs for Canada and Mexico.

"We're not trying to blow up the world. There's no intention of that," Ross said in an interview with CNBC's "Squawk Box." "The president indicated the other day he has a willingness to provide an exemption to Canada and Mexico."

"We're not looking for a trade war. We're going to have very sensible relations with our allies," Ross added. "We hope and we believe that at the end of the day, there will be a process of working with the other countries that are our friends."

A few hours before Ross spoke, the European Union outlined a three-pronged retaliation for the proposed Trump tariffs. It said such U.S. imports as peanut butter, cranberries and orange juice could see higher charges in Europe.

In a tweet on Monday, Trump dangled the possibility of dropping his call for steel and aluminum tariffs if NAFTA is renegotiated to terms more favorable to the U.S.

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During a hearing with Congress on Tuesday, Treasury Secretary Steven Mnuchin indicated that once a new NAFTA deal is reached, the trading partners wouldn't be subject to the tariffs.

Ross dismissed the notion that Gary Cohn's resignation Tuesday night as Trump's top economic advisor was part of a "palace coup." Cohn had clashed with Trump's protectionist advisors on the issue of tariffs.

"He's done very good work on the taxes, he's done very good work on the infrastructure," Ross told CNBC. "Gary, as you know from all kind of media, has been contemplating some sort of a move for some little while."

The Commerce Department recommended imposing heavy tariffs or quotas on foreign producers of steel and aluminum last month in the interest of national security. Ross said at the time that steel is important to U.S. national security and that current import flows are adversely affecting the steel industry.

The Commerce secretary "concludes that the present quantities and circumstance of steel imports are 'weakening our internal economy' and threaten to impair the national security," the department said Feb. 16.

Shortly after Trump announced the tariffs, Ross told CNBC the plan for tariffs of 25 percent on imported steel and 10 percent on aluminum products is "no big deal." He used cans of Campbell's Soup and Coca-Cola to stress his point about what he called insignificant price increases from Trump's tariffs.