By next year's anniversary, Bloomberg will be out of office, and the museum is expected to be open beneath the memorial plaza.
While the memorial honors those killed, the museum is intended to present a broader picture of 9/11, including the experiences of survivors and first responders.
But the organizers expect they "will always keep the focus on the families on the anniversary," Daniels said.
That focus was clear as relatives gathered last September on the tree-laden plaza, with a smaller crowd than in some prior years.
After the throng and fervor that attended the 10th anniversary, "there was something very, very different about it," said Charles Wolf, whose wife, Katherine, was killed in the trade center's north tower. "It felt almost cemetery-ish, but not really. It felt natural."
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Associated Press writers Verena Dobnik and Jim Fitzgerald contributed to this report.
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