A key White House adviser on faith issues said Tuesday that several organizations with ties to the administration have approached President Obama’s aides about finding a resolution to fast-growing controversy over a new rule requiring many Catholic institutions to offer birth control and other contraception services as part of employees’ health care coverage.

“There are conversations right now to arrange a meeting to talk with folks about how this policy can be nuanced,” said Pastor Joel C. Hunter, a Florida megachurch pastor who has grown personally close to Obama and advised his White House on religious issues. “This is so fixable, and we just want to get into the conversation.”