WASHINGTON—The Trump administration said it was no longer considering pulling out of the North American Free Trade Agreement, following a day of intense lobbying from business leaders and lawmakers who rallied to quash internal White House discussion of the prospect.

The White House said in a statement issued late Wednesday night that President Donald Trump had called his Mexican and Canadian counterparts following widespread reports he was considering pulling out of the 23-year-old pact that stitches the three economies tightly...