“Now in some parts of the world, there is a move toward protectionism,” Toshimitsu Motegi, the Japanese economy minister, said in Tokyo, announcing the agreement of the Trans-Pacific Partnership, redrafted after Mr. Trump pulled the U.S. out a year ago. “TPP-11 is a major engine to overcome such a phenomenon.”

The debate is expected to intensify this week as it shifts to Davos, Switzerland, where Mr. Trump is scheduled Friday to explain and defend his emerging “America First” policies to the World Economic Forum, a group that has staunchly defended and fostered globalism over the past four decades.

As a sign of the arguments to come, Prime Minister Narendra Modi of India addressed the forum Tuesday with a speech that didn’t mention Mr. Trump by name, but appeared aimed at him.

“Many societies and countries are becoming self-focused. Globalization is shrinking,” Mr. Modi said, adding that this trend was as grave a challenge as terrorism. “Protectionism and its forces are rearing their heads.”

In response to criticism of Mr. Trump’s trade policy, Gary Cohn, the head of the White House National Economic Council, said Tuesday: “Look, the U.S. is pulling back from nothing.” He added: “American first does not mean America alone.”

U.S. officials said that as they put forth more aggressive trade policies in the coming weeks, they will also try to persuade skeptical allies that their actions are intended to improve the international economic system, not destroy it. The underlying message: The U.S. is neither retreating from trading partners nor fighting them.

“A strong U.S. economy benefits the world, having fair and reciprocal trading relationships help the world, and the U.S. is engaged in trying to help the global economy through reforms like that,” a White House trade official said. “That’s a message you’re going to see us using more frequently in the near future.”

Mr. Trump’s emerging trade policy involves three main components, each advanced in different forms this week.

The first is ramping up trade-enforcement actions, like the broad, steep tariffs announced Monday aimed at protecting U.S. makers of solar panels and washing machines. Administration officials said more of these types of protections are coming, with studies under way for action on steel and aluminum.

The U.S. also plans to assess action against an array of Chinese goods and investments in retaliation for China allegedly pressuring U.S. companies to turn over valuable intellectual property.

“You’ll see what’s going to take place over the next number of months,” Mr. Trump said during an Oval Office ceremony held Tuesday to sign the solar and washer actions.

The second part of the trade agenda is either shunning pacts negotiated by previous administrations, like TPP, or rewriting them. A large delegation of U.S. trade negotiators is in Montreal this week to press Canada and Mexico for concessions to rebalance the North American Free Trade Agreement in ways aimed at steering manufacturing from Mexico back to the U.S.

Mr. Trump’s chief trade negotiator, Robert Lighthizer, has indicated that if his counterparts don’t show sufficient compromise in this round, Mr. Trump will be more inclined to pull the U.S. out of the quarter-century-old pact.

“Nafta is moving along pretty well,” Mr. Trump said Tuesday, but added: “I happen to be of the opinion that if it doesn’t work out, we’ll terminate it.”

The third element of the policy agenda is to shake up the World Trade Organization, the overseer of the global trading system since 1995. Administration officials said the Geneva body too often rules against U.S. interests, and doesn’t do enough to rein in China’s state-driven trading system.

To make its point, the U.S. is blocking appointments to the WTO’s court responsible for arbitrating trade disputes between members, a move that risks gumming up the world commercial legal system.

In a tense meeting of world trade officials in Geneva on Monday, Mexico introduced a proposal backed by nearly 60 WTO members demanding the U.S. end its filibuster. Eighteen delegates—including those from Canada, Europe, and China—spoke to support the proposal, one warning of “major consequences” for the WTO. The U.S. representative declined to yield.

As the administration advances those three goals, officials are honing their message for how they plan to explain the significant shifts in U.S. international economic policy to allies and trading partners.

One theme: “We’re not turning away from the system, we’re saying the system needs to be reformed to survive,” the White House trade official said.

Mr. Trump said Tuesday: “There won’t be a trade war.”

Indeed, many trading partners are sympathetic to one aspect of the Trump administration’s criticism: that the WTO doesn’t do enough to counter Beijing’s government-driven industrial policy. That policy has helped fuel Chinese exports and growing market shares that have destroyed vital industries abroad, from steel to semiconductors. Both the European Union and Japan have recently joined with the U.S. in efforts to get the WTO to more directly pressure China.

And many free-trade advocates find criticism from leaders like Mr. Modi ironic, given India’s long history of protectionism and its own fights with the WTO.

But the U.S. challenge is to avoid alienating those countries as Washington either hits them with new trade barriers or rejects longstanding trade arrangements with them.

While Mr. Trump has criticized multilateral trade agreements like TPP, Mr. Cohn said that the administration is eager to expand global trade through bilateral agreements and said that Mr. Lighthizer “is working on a bunch of different agreements.”

Mr. Cohn declined, though, when pressed to identify any specific agreements under way, and countries the administration has identified as priorities for new trade pacts, such as Japan, have actively shunned overtures for a new bilateral pact.

Japan and other TPP participants have instead chosen to strike new deals elsewhere.

Since Mr. Trump’s inauguration last year, the EU has accelerated a campaign to sign new free-trade agreements around the world, seeking to fill what it sees as a new void in advancing market-opening agreements.

While U.S.-EU talks launched under former President Barack Obama, a Democrat, have been stalled since 2016, the EU implemented new pacts last year with Japan and Canada. The EU is seeking this year to build on that by clinching deals to slash tariffs and open new markets from Mexico to Chile. The EU is also negotiating a trade deal with the Mercosur bloc comprising Argentina, Brazil, Paraguay and Uruguay.

Meantime, both Canada and Mexico signed onto the new TPP pact, with some officials seeing it as a hedge to open non-American markets if Nafta collapses.

The U.S. withdrawal from TPP—which also includes Singapore, Brunei, New Zealand, Chile, Australia, Peru, Vietnam, and Malaysia—and its hard-edge negotiating over Nafta have “prompted governments and stakeholders across the region to reassess their reliance on American economic leadership and the U.S. market,” the Asia Society Policy Institute wrote in a recent report. U.S. allies, the report added, are “hard at work developing contingency plans for…advancing trade and investment liberalization without the United States.”

—Emre Peker in Brussels contributed to this article.

Write to Jacob M. Schlesinger at [email protected]

Corrections & Amplifications 
Negotiations between the U.S. and European Union over a free-trade agreement stalled in 2016, before Donald Trump became president. A previous version of this article incorrectly stated that the talks had stalled in the Trump administration. (Jan. 24, 2018)