By David Lawder and Andrea Shalal

WASHINGTON (Reuters) - U.S. President Donald Trump on Tuesday vowed to hit the European Union with tariffs and said his administration was discussing a 10% punitive duty on Chinese imports because fentanyl is being sent from China to the U.S. via Mexico and Canada.

Trump voiced his latest tariff threats in remarks to reporters at the White House a day after taking office without immediately imposing tariffs as he had promised during his campaign.

Financial markets and trade groups exhaled briefly on Tuesday, but his latest comments underscored Trump's longstanding desire for broader duties and a new Feb. 1 deadline for 25% tariffs against Canada and Mexico, as well as duties on China and the EU.

Trump said the EU and other countries also had troubling trade surpluses with the United States.

"The European Union is very, very bad to us," he said, repeating comments made Monday. "So they're going to be in for tariffs. It's the only way ... you're going to get fairness."

Trump said on Monday that he was considering imposing the duties on Canada and Mexico unless they clamped down on the trafficking of illegal migrants and fentanyl, including precursor chemicals from China, across their U.S. borders.

Trump had previously threatened a 10% duty on Chinese imports because of the trade, but realigned that with the Feb. 1 deadline.

White House trade adviser Peter Navarro told CNBC early on Tuesday that Trump's Canada and Mexico tariff threat was to pressure the two countries to stop illegal migrants and illicit drugs from entering the U.S.

"The reason why he's considering 25, 25 and 10 (percent), or whatever it's going to be, on Canada, Mexico and China, is because 300 Americans die every day" from fentanyl overdoses, Navarro said.

Trump on Monday announced a sweeping immigration crackdown, including a broad ban on asylum.

APRIL 1 REPORTS

Trump on Monday signed a broad trade memorandum ordering federal agencies to complete comprehensive reviews of a range of trade issues by April 1.

These include analyses of persistent U.S. trade deficits, unfair trade practices and currency manipulation among partner countries, including China. Trump's memo asked for recommendations on remedies, including a "global supplemental tariff," and changes to the $800 de minimis duty-free exemption for low-value shipments often blamed for illicit imports of fentanyl precursor chemicals.

The reviews ordered create some breathing room to resolve reported disagreements among Trump's cabinet nominees over how to approach his promises of universal tariffs and duties on Chinese goods of up to 60%.

Trump's more measured approach to tariffs fueled a rally in U.S. stocks that pushed the benchmark S&P 500 index to its highest level in a month, though Trump's new salvo on China and the European Union may deflate that momentum.

Trump likely "decided to go a little slower and also to make sure he has as firm a legal foundation as he can get for these kinds of actions," said William Reinsch, a trade expert at the Center for Strategic and International Studies in Washington. "He's figuring out how to best use his leverage to get what he wants."

SOFTER TONES

Mexico and Canada struck conciliatory tones in response to Trump's Feb. 1 deadline. Mexican President Claudia Sheinbaum said that she would emphasize Mexico's sovereignty and independence and would respond to U.S. actions "step by step."

But she added that the U.S.-Mexico-Canada free trade agreement was not up for renegotiation until 2026, a comment aimed at pre-empting suggestions that Trump will seek an early revamp of the pact that underpins over $1.8 trillion in annual three-way trade.

Corn farmers are worried about U.S. tariffs and retaliatory duties disrupting trade with Mexico, their top export customer for corn, and with Canada, the top export customer for U.S. corn-derived ethanol.

"We understand that he is a negotiating type of person," Illinois farmer Kenny Hartman Jr, board president of the National Corn Growers Association, said of Trump. "We're just hoping that we can come out of this where we don't lose the exports - we don't lose that corn going to Mexico or that ethanol going to Canada."

(Reporting by David Lawder, Andrea Shalal and Steve Holland; Writing by David Lawder and Ryan Patrick Jones; Editing by Lisa Shumaker and Leslie Adler)