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Mr. McCaul also said that the Chechen rebels, who have been engaged for decades in a conflict with Russia in the majority-Muslim province, are “some of the fiercest jihadist warriors out there.”

Some also are questioning how the FBI, which reportedly interviewed Tamerlan Tsarnaev, missed the warning signs.

Mr. Graham said the fact that he traveled to Chechnya and talked online about killing American citizens should have tipped off authorities.

“Either our laws are insufficient or the FBI failed, but we’re at war with radical Islamists and we need to up our game,” he said on CNN.

Mr. King echoed those sentiments, arguing that political correctness must not get in the way of a full investigation into whether the brothers were working as part of a larger Muslim terrorist organization.

“Ninety-nine percent of Muslims are outstanding Americans, but the fact is, that’s where the threat is coming from,” he said.

Boston’s Muslim community has strongly condemned the attacks. The Islamic Society of Boston Cultural Center said in a statement over the weekend that the city’s Muslims are “angry” about the bombings and “hurt” by the fact they could not prevent the attacks.

• Susan Crabtree contributed to this report.