"It is a time for cool heads, calm nerves," he said. "What happened on Tuesday was an attack not just on the United States, but an attack on the civilized world."
He added: "I can assure you, the whole of Europe will stand together" with the US.
Blair confirmed that the death toll of Britons, probably 200 to 300, among the dead would be the highest in any attack since the end of World War II.
Asked about building widespread support for possible military strikes, the prime minister went on: "This is something obviously we discussed with the American president.
"Secondly, there has to be an agenda we construct at an international level to dismantle the machinery of international terrorism."
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