President Obama on Thursday ordered intelligence agencies to take a series of steps to streamline how terrorism threats are pursued and analyzed, saying the government had to respond aggressively to the failures that allowed a Nigerian man to ignite an explosive mixture on a commercial jetliner on Christmas Day.

Janet Napolitano, secretary of homeland security, spoke about security changes on Thursday.

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President Obama pledged not to “succumb to a siege mentality,” sacrificing civil liberties, but called for expanding the criteria for adding people to watch lists.

The president...