As corporations and public officials ratcheted up pressure on Indiana over its days-old religious-objections law, state lawmakers on Monday said they would try to find a way to clarify that the measure wouldn’t allow discrimination against gays and lesbians.

The speaker of Indiana’s state House, Brian Bosma, and the Senate president pro tem, David Long, both Republicans, said they are working with their caucuses and GOP Gov. Mike Pence on the proposed language of what they are describing as a clarifying measure. They said...