In Indianapolis on Wednesday, lawmakers were weighing language they intend to add to the state’s law as part of what Mr. Pence has described as “a clarification” and also “a fix.” Precise wording was still being hashed out, officials said, but Mr. Pence has said that the intent will be to clarify that the state’s law does not give businesses the right to deny services to anyone, including gay men and lesbians

With the N.C.A.A. Final Four tournament in Indianapolis this weekend and mounting pressure from business leaders, Indiana lawmakers were racing to draft new language, then hurry the revised measure through both chambers of the state legislature for Mr. Pence’s signature before week’s end.

To expedite the process, aides said legislators were expected to use an unrelated, but almost-approved Senate bill as a vehicle for the new language. That would allow them to reach agreement on language during a committee meeting of selected lawmakers, then move the measure through both chambers immediately.

Still, Democrats, who hold the minority, have said they intend to push for a repeal, and it remained uncertain whether all Republicans would l support what some conservatives in the state view as a watered-down measure.

The bill in Arkansas is similar to the Indiana law, but both diverge in certain respects from the federal Religious Freedom Restoration Act. That act was passed in 1993 and signed into law by President Bill Clinton, Arkansas’s most famous political son.