WASHINGTON — Faith in American leadership has plunged in many nations around the world in the months since President Trump took office, according to a new survey, underscoring the challenges facing the new president as he prepares to make his second overseas trip next week.

Just 22 percent of those interviewed outside the United States expressed confidence in Mr. Trump to do the right thing, compared with 64 percent who had similar confidence in the late stages of President Barack Obama’s administration, according to the Pew Research Center. In only two of 37 countries in the survey did Mr. Trump fare better than Mr. Obama: Russia and Israel.

“Trump and many of his key policies are broadly unpopular around the globe, and ratings for the U.S. have declined steeply in many nations,” the center said in a report released on Monday. “The sharp decline in how much global publics trust the U.S. president on the world stage is especially pronounced among some of America’s closest allies in Europe and Asia, as well as neighboring Mexico and Canada.”

The findings come despite concerted efforts by Mr. Trump to build relationships with world leaders. On Monday, he met with Prime Minister Narendra Modi of India at the White House and he is scheduled to host President Moon Jae-in of South Korea for a two-day visit starting on Thursday. As president, he has brought the leaders of China and Japan to his Mar-a-Lago estate in Florida and telephoned other world leaders dozens of times.