President Obama assured the rest of the world Thursday that America will overcome the “crude populism” of the far left and far right that has surfaced in this year’s presidential campaign, and said voters will reject Donald Trump’s argument that the U.S. system is “rigged.”

Writing in The Economist, Mr. Obama said “a certain anxiety” about immigration and globalization has taken hold in the U.S., emerging in “a strain of anti-immigrant, anti-innovation protectionism.”

At home and abroad, the president, said, people continually ask him why “some on the far left and even more on the far right embraced a crude populism that promises a return to a past that is not possible to restore — and that, for most Americans, never existed at all.” It was an obvious reference to the campaigns of Sen. Bernard Sanders of Vermont and Mr. Trump, the Republican nominee.

As a result of wage inequality and the financial crisis of 2008, Mr. Obama said, “it’s no wonder that so many are receptive to the argument that the game is rigged.” He cautioned that much of Americans’ frustration is “fanned by politicians who would actually make the problem worse rather than better.”

The president said discontent in the U.S. “is driven by fears that are not fundamentally economic.”

“The anti-immigrant, anti-Mexican, anti-Muslim and anti-refugee sentiment expressed by some Americans today echoes nativist lurches of the past — the Alien and Sedition Acts of 1798, the Know-Nothings of the mid-1800s, the anti-Asian sentiment in the late 19th and early 20th centuries, and any number of eras in which Americans were told they could restore past glory if they just got some group or idea that was threatening America under control,” he said. “We overcame those fears and we will again.”

The president pointed to steady job growth, falling poverty rates and rising income in the U.S. as signs that the America economic model still works.

Mr. Obama said his successor must understand that America’s economy cannot be redesigned by “breaking up all the biggest banks or erecting prohibitively steep tariffs on imports.” Instead, he said the U.S. must boost productivity growth, combat rising inequality, ensure that “everyone who wants a job can get one” and build a “resilient” economy.

To do that, Mr. Obama said the U.S. must overcome “an anti-tax ideology that rejects virtually all sources of new public funding” and “a fixation on deficits at the expense of the deferred maintenance bills we are passing to our children, particularly for infrastructure.” During his presidency, the total national debt has risen from $10.6 trillion to nearly $20 trillion.

He also chided “a political system so partisan that previously bipartisan ideas like bridge and airport upgrades are nonstarters.”

“America’s political system can be frustrating. Believe me, I know,” Mr. Obama said. “But it has been the source of more than two centuries of economic and social progress. The progress of the past eight years should also give the world some measure of hope.

“For all the work that remains, a new foundation is laid.”