WASHINGTON (Reuters) - The Trump administration is talking to all major trading partners throughout the world about ways to bring down President Donald Trump's new tariffs, Commerce Secretary Howard Lutnick said on Thursday, adding that they will have to change their rules to allow more imports of U.S. products.

Lutnick told CNBC television a day after Trump announced a 10% global baseline tariff and steep reciprocal duties that the discussions had been going on for more than a month.

"The key is, will they take our agricultural products? Will they treat us fairly? Can they treat us fairly? And the answer is, over time, that is going to be yes," Lutnick told CNBC television. "American products are going to be better sold elsewhere in the world."

Lutnick said that he did not believe that countries would be able to win exemptions from the tariffs, and it will not be "effective for the world to retaliate" against the U.S. But the Trump administration would engage in discussions to find ways to treat U.S. goods more fairly.

This includes ways to eliminate trade barriers such as those posed by value-added tax, which Lutnick said acted as subsidies for exports. He added that at least one trade minister offered to allow U.S. vehicles to access similar subsidies, without identifying the country.

"I expect most countries to start to really examine their trade policy towards the United States of America, and stop picking on us," Lutnick said. "Stop saying that we can't sell our corn to India. Stop saying that we can't sell our beef anywhere."

(Reporting by David Lawder; Editing by Alison Williams and Nick Zieminski)