The U.S. tariff rate for some countries will go up to 15% or higher from the newly-imposed 10%, U.S. Trade Representative Jamieson Greer said on Wednesday, without naming any specific trading partners or other details.

"Right now, we have the 10% tariff. It'll go up to 15 (%) for some and then it may go higher for others, and I think it will be in line with the types of tariffs we've been seeing," Greer said in an interview on Fox Business Network's "Mornings with Maria" program.