WASHINGTON — Much of the world has soured on American leadership since President Trump took office, a loss of faith that has opened up opportunities for other countries like China, Russia and Germany to assert themselves on the international stage, according to an extensive new survey of people living around the globe.

Just 30 percent of people interviewed in 134 countries last year approved of American leadership under Mr. Trump, a drop of nearly 20 percentage points since President Barack Obama’s final year and the lowest finding since the Gallup polling organization began asking the question overseas more than a decade ago. The decline was especially steep in Latin America, Europe and Canada.

The findings of the survey come just a week before Mr. Trump plans to go to Europe to attend the annual World Economic Forum in Davos, Switzerland, a traditional gathering of political and economic elites. Mr. Trump has alienated many other countries, including longtime American allies, by pulling back from international agreements and organizations, not to mention by issuing derogatory remarks like those last week denigrating Africa and Haiti.

“It makes it more challenging to lead when people are this down on your leadership,” said Jon Clifton, Gallup’s global managing partner. “But on the other hand, if we were sitting with President Trump and his leadership team, they would say these results are understandable because we’re making tough decisions.”