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House Speaker John A. Boehner on Thursday criticized the administration’s decision.

“This mandate violates our Constitution. I think it violates the rights of these religious organizations, and I would hope that the administration would back up and take another look at this,” said the Ohio Republican during his weekly briefing with reporters.

House Minority Leader Nancy Pelosi, who, like Mr. Boehner is Catholic, said Thursday she supports the administration’s decision.

Sean Lengell and Paige Winfield Cunningham contributed to this report.