WASHINGTON—The Trump administration faces a deadline at the end of next week on whether to approve a scientific report that verifies climate change and attributes it to humans, a position that contradicts some of the rhetoric the president used during his 2016 campaign.

The White House’s Office of Science and Technology Policy is supposed to decide by Aug. 18 whether to approve or recommend changes to the “Climate Change Special Report,” the research on climate science that feeds its National Climate Assessment. That document,...