The Trump administration has set the stage for weeks of heightened tension between the U.S. and its trading partners as administration officials race to meet self-imposed deadlines to complete a series of high-stakes negotiations with China, Mexico, Canada and Europe.

A U.S. trade delegation left Tuesday for China hoping to glean trade concessions from Beijing, while earlier in the day U.S. Trade Representative Robert Lighthizer confirmed, after months of wrangling with Mexico and Canada, a mid-May deadline for the renegotiation of the North American Free Trade Agreement. And the administration set a new June 1 deadline to come to an agreement with European officials on steel and aluminum tariffs.

The developments position May as a crucial month for President Donald Trump to fulfill a campaign promise to rewrite the rules of trade, with the aim of reducing U.S. deficits and protecting American workers. The combative approach to trade has been popular with Mr. Trump’s base—and many Democrats—but has heightened economic uncertainties that are likely to spark more volatility in the stock and commodities markets.

Mr. Trump has delegated the details of these trade initiatives to Mr. Lighthizer and other senior administration officials, from Commerce Secretary Wilbur Ross to Treasury Secretary Steven Mnuchin. But he also has made clear that the key to success rests with the president alone, an unpredictable negotiator who rarely shows his hand.

“The discussions will take place in Beijing,” said senior White House adviser Peter Navarro, before jumping on a flight to Beijing, but “the decisions will take place in Washington.”