Chambliss Sen. Saxby Chambliss (R-Ga.). (Alex Wong/Getty Images)

Sen. Saxby Chambliss (R-Ga.), the vice chair of the Senate Intelligence Committee, said Sunday that the recent signs of a potential terrorist attack are the "most serious threat I’ve seen in the last several years.”

The issue prompted the United States to close many of its embassies over the weekend and issue a warning to Americans traveling abroad.

The U.S. State Department on Sunday extended the closure through Saturday for 19 embassies, consulates and smaller posts “out of an abundance of caution,” spokeswoman Jen Psaki said in a written statement. Several other posts, including embassies in Kabul and Baghdad, will be allowed to reopen Monday.

“There has been an awful lot of chatter out there," Chambliss said on NBC's "Meet the Press". "Chatter means conversation about terrorists, about the planning that’s going on, very reminiscent of what we saw pre-9/11. We didn’t take heed on 9/11 on the way that we should [have]. But here, I think it’s important that we do take the right kind of planning as we come to the close of Ramadan, we know that’s always an interesting time for terrorists."

Pressed for details about the threat, Chambliss said: "What we have heard is some specifics on what’s intended to be done and some individuals who are making plans, such as we saw before 9/11. Whether they are going to be suicide vests that are used, or whether they’re planning on vehicle-borne bombs being carried into an area, we don’t know. But we’re hearing some kind of that same chatter that we heard pre-9/11 leading up to anecdotes like that, taking place by the terrorists."

Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, said Sunday on ABC's "This Week" that the potential for an attack is serious.

“There is a significant threat stream, and we're reacting to it,” he said. Asked for details about what the threat entails, the general said: “That part of it is unspecified, but the intent seems clear. The intent is to attack Western, not just U.S. interests.”

Lori Montgomery contributed to this post.