Ridge said al-Qaida cells or sympathizers probably were still in America. Even if those networks were destroyed, other terrorists could take their place, he said.
"We will get Osama bin Laden and we will dismantle al-Qaida, but I'm afraid that there will be successor organizations, and we have to be prepared to deal with them," Ridge said on CNN's "Late Edition."
Ridge said the country was "safer, stronger and more secure" since Sept. 11, but more terrorist attacks are possible.
"I can't tell you absolutely, conclusively, without any doubt that there are X number of al-Qaida operatives here," Ridge said. "But what we do know is that we are an open and a welcoming and trusting country. And I think we should operate under the assumption that there are still some sympathizers or cells in the United States."
Sen. John Edwards, D-N.C., a member of the Senate Intelligence Committee, agreed with Ridge's analysis.
"It would be a reasonable assumption that there are still terrorist cells in the United States," Edwards said on CNN. "We need to stay focused on that."
Foreign terrorists probably weren't responsible for last fall's anthrax attacks, Ridge said. He said investigators were looking at domestic sources.
"I think a lot of us, including myself, felt that it couldn't possibly be a coincidence after Sept. 11," Ridge said. "I think our natural inclination was to look to external terrorists, but the primary direction of the investigation is turned inward."
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