This morning on "This Week," Rep. Peter King told Martha Raddatz that the attack yesterday on an upscale mall in Nairobi, Kenya that left 59 people dead and nearly 200 wounded was "very sophisticated" and shows the ongoing ability of al Qaeda and its affiliates to inflict terror.

"This is a particularly brutal attack and it almost seems as if the terror world is coming full cycle. Because one of the first major attacks that we recall against the United States was the attacks on the embassies back in 1998 and now we have 15 year later a massacre," King said on "This Week." "Really a well coordinated, well planned, horrific massacre. They attacked at the busiest time of the week, the busiest time of the day. They knew what they were doing, they took the hostages."

"So this is again very similar to Mumbai, and showing that al Qaeda and its affiliates are still extremely powerful and still able to really strike terror into the hearts of people," King added. "Attacking at a shopping mall, that has no military significance at all, this is clearly an attack to terrorize and murder innocent civilians. And if the reports are true that they're allowing Muslims to leave and focusing on non-Muslims, again they're making this part of their jihadist war."

King said "all indicators" point toward the Somali-based terrorist group al-Shabab - which has claimed responsibility - having carried out the attack, adding that the group has actively recruited in the U.S.

"It's an extremely deadly organization, very well trained. And it's one of the only al Qaeda affiliates which actually has actively recruited here in the United States," King said. "There is at least 40 to 50 Somali-Americans who have gone from the United States to Somalia to be trained. A number of them have been killed but there's others still alive. So I would assume that the FBI and local law enforcement are looking into those Somali-American communities today, any leads or indicators, using all their sources and resources to make sure that there is no follow up attempt here in the United States."

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King said he had not heard whether or not Somali Americans were involved in the attack on the Westgate mall in Nairobi, but said the attack shows the "growing influence" of al Qaeda in Africa.

"We know there's probably still 15-20 Somali Americans who are still active over there. The concern would be if any of them have come back to the United States and would use those abilities here in the United States," King said. "This shows, I think, the really growing influence of al Qaeda in Africa. We have al-Shabab now in Somalia going off into Kenya, carrying out an attack outside of its own country. For years the State Department did not want to declare al-Shabab a terrorist organization because they thought it was just focusing on tribal issues within Somalia."

"Now we see by attacking Kenya, they certainly have an international dimension to them," King added. "You also have Boko Haram in Nigeria and also you have al-Shabab working closely with al Qaeda in the Arabian Peninsula in Yemen. We're talking about very significant terrorist groups here which are showing a capacity to attack outside their borders and actually recruit people from here in the United States."

Asked about implications for the U.S. homeland, a senior law enforcement official told ABC News that U.S. intelligence shows no heightened threat to the United States as a result of the Nairobi attack.

In fact, the official said, the latest analysis indicates al-Shabab is focused on actions in East Africa and does not have the capability to strike inside the United States, even if it had the desire to do so.

In an exit interview with ABC News' Pierre Thomas earlier this month, recently departed FBI director Robert Mueller said the threat emanating from Somalia had "died down somewhat."

ABC's Mike Levine contributed to this story

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