Cracks are forming in the coalition Facebook Inc. assembled to build a global cryptocurrency-based payments network.

Visa Inc., Mastercard Inc. and other financial partners that signed on to help build and maintain the Libra payments network are reconsidering their involvement following a backlash from U.S. and European government officials, according to people familiar with the matter. Wary of attracting regulatory scrutiny, executives of some of Libra’s backers have declined Facebook’s requests to publicly support the project,...