Last Updated Jan 8, 2015 4:23 PM EST
CBS News has learned that the two brothers suspected in the massacre at a French satirical newspaper this week have connections to Yemen and previous links to al Qaeda in Iraq.
It was not immediately clear whether it was Said or Cherif Kouachi, both in their early 30s, who traveled to Yemen in 2011, but a senior intelligence source told CBS News on Thursday that both men are known long-term jihadists, and were known to French officials.
Cherif Kouachi was convicted in 2008 of recruiting fighters in France to go and fight in Iraq. He was jailed for 18 months.
In addition, U.S. officials tells CBS News that both men were on the U.S. no fly list and a broader terror watch list.
Both brothers had been known previously to French intelligence officials.
Al Qaeda in the Arabian Peninsula (AQAP), the branch of the terror network considered to represent the most immediate threat to the U.S. and other Western nations, is based in Yemen. A witness to the attack on Wednesday said one of the men claimed to be acting on behalf of "al Qaeda in Yemen" during the shooting.
Former CIA deputy director and CBS News senior security contributor Mike Morell said Thursday on "CBS This Morning" that "there's a good possibility we're looking at an al Qaeda in Yemen-directed attack."
"I think it's actually the most dangerous terrorist group out there," said Morrell of AQAP. "They said just a few days ago that they want to conduct attacks against the West, so the head of the snake has not been cut off. The threat continues."
The al Qaeda branch was behind the attempt to blow up an aircraft over Detroit on Christmas Day 2009.
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Morell said the significance of one of the suspects' trip to Yemen is that the individual most likely received training.
"We saw that yesterday in the military-style, the commando-style attack - very sophisticated," Morell said.
AQAP is different from ISIS, Morell said.
"In fact, they're in competition with each other for prominence, for fundraising - very different," he said.
John Miller, the deputy commissioner of intelligence and counterterrorism for the New York Police Department, described the different models each operated by.
"One is the ISIS model - their job is to take territory and hold it, plant a flag and say, 'This is the Islamic State.' They're in the nation-building business right now as a terrorist organization," Miller said. "Al Qaeda of the Arabian Peninsula ... their job is as an external planning and operations node for al Qaeda."
After U.S.-led war and drone strikes chipped away its leadership in Afghanistan and Pakistan, Miller said al Qaeda "kind of handed the ticket to AQAP in Yemen and said, 'Your job is to attack the United States and its allies in the West.'"
Morell described the terror attack in Paris as "a moment" of significance .
"This was an attack on our very way of life. This was an attack on freedom of speech. So this was an attack on the way the West lives, and that's different than what we've seen before," Morell said.
"And I think the response you see in the street and around the world is a reflection of that. The other thing, I think, as 9/11 in New York, the subway bombings in London and now this in Paris, this tells everybody that this can happen everywhere."