Mayor Bill de Blasio, welcoming federal-government tenants back to the rebuilt World Trade Center 15 years after the 9/11 attacks, said on Friday that “the terrorists lost, and they lost badly.”

More than 1,000 federal workers will staff six floors of One World Trade Center, which stands a symbolic 1,776 feet high, the tallest skyscraper in the Western Hemisphere.

The federal tenants are U.S. Customs and Border Protection, the Federal Emergency Management Agency and the General Services Administration, GSA spokeswoman Ashley Nash-Hahn said. The government has a 20-year lease on about 220,000 square feet, paying $15 million a year. It had been an original World Trade Center tenant starting in the 1970s.

De Blasio told dignitaries at Friday’s ceremony that Ground Zero’s rebuilding helps show that “the terrorists achieved none of their aims.”

“In fact,” he said, “you could even say the terrorists’ plan backfired.”

Cardinal Timothy Dolan, the archbishop of New York, gave the ceremony’s invocation and afterward called de Blasio’s remarks “very insightful.”

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“What they wanted for violence and destruction and division and fear to reign hasn’t happened,” he said of the 9/11 attackers. “I think America is stronger than that.”

Whether the attackers succeeded or failed is “a very complicated question,” said Max Abrahms, an assistant professor of political science at Northeastern University, where he’s studied terrorism’s effectiveness.

While al-Qaida has failed in its stated political goals, such as hastening the United States’ withdrawal from the Persian Gulf and harming the country’s relationship with Israel, he said, the group could be seen to have succeeded in other ways, by provoking an overreaction to the 9/11 attacks and radicalizing sympathetic Muslims.

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Richard Bulliet, an emeritus history professor at Columbia University, said de Blasio’s words about resilience represent “a very positive statement of America’s will to get past 9/11 — but that does not erase 9/11.”

The attackers “achieved their most long-lasting aim, simply by making the entire country hyperaware of the dangers” of terrorism, Bulliet, a Middle East specialist who has been a consultant to police forces about terrorism. “The philosophical basis for terrorism is to have a goal of creating a climate of fear in the target population, and they certainly have created a climate of fear.”

Meanwhile, presiding over Friday’s ceremony was U.S. Homeland Security Secretary Jeh Johnson, whose agency is locked in a funding dispute with the city over terrorism-prevention money.

The Obama administration has said that much of the money the federal government gives the region under one such prevention program has remained unspent, but the city has countered that the money is spent or being spent. U.S. Rep. Steve Israel (D-Huntington)’s office has said the loss could be about $80 million.

On Friday, Johnson told Newsday: “We had to make some tough choices to meet the budget caps set by Congress.”

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Asked whether the region’s leaders would be satisfied with the ultimate funding for terrorism prevention, he said: “I believe that when the budget process is complete, we’ll be in a good place.”