Monsanto Co. pressed the EPA in 2015 to publicize a report that would show its Roundup herbicide doesn’t cause cancer, but the agency appeared reluctant to do so on the company’s timeline, newly released documents show.

The correspondence, part of a cache of documents posted Aug. 1 by attorneys representing cancer patients in multidistrict litigation against Monsanto, is an attempt to showcase what the attorneys claim is an inappropriately close relationship between the Environmental Protection Agency and Monsanto. But it also shows an agency whose leaders under President Barack Obama were in no hurry to put out a key report...