Three big companies quit an influential lobbying group that had focused on shaping climate-change legislation, in the latest sign that support for an ambitious bill is melting away.

Oil giants BP PLC and ConocoPhillips and heavy-equipment maker Caterpillar Inc. said Tuesday they won't renew their membership in the three-year-old U.S. Climate Action Partnership, a broad business-environmental coalition that had been instrumental in building support in Washington for capping emissions of greenhouse gases.

The...