ATLANTA -- Two passenger planes were escorted by fighter jets to Atlanta's airport Saturday afternoon after bomb threats were made against them, authorities said.

Late Saturday, the airport posted to its Twitter account that both planes had been cleared and that normal airport operations had resumed.

Delta Air Lines Flight 1156 from Portland, Oregon, and Southwest Airlines Flight 2462, arriving from Milwaukee, landed at a remote location at Hartsfield-Jackson International Airport, the airlines confirmed to CBS News.

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"Due a security situation, the aircraft operating Flight 2492 was taken to a remote area of the airport where customers and the aircraft are being rescreened," Southwest spokesman Dan Landson said. "Our number one priority is the safety of our customers and people. We cannot comment on the nature of the security situation."

A Delta spokesperson confirmed one of their planes was also involved and that the aircraft was being inspected.

NORAD spokesman Preston Schlachter told CBS News two NORAD fighter jets escorted the planes as a precautionary measure. He would not confirm any additional details.

FBI Special Agent Stephen Emmett in Atlanta said both flights were "safely on the ground."

"Earlier, airline officials received a bomb threat and precautions were taken, to include the scrambling of military aircraft via NORAD, having deemed the threats as credible," Emmett told CBS News. "Explosives units at Atlanta are now on scene to sweep the aircraft."

CBS affiliate WGCL in Atlanta reported the threats were made on Twitter, with the first message sent to Delta at noon EST.

"I have a bomb on one of your planes, but I forgot which one when I left the airport," one message read. "Can you help me find it?"

According to WGCL, the person claimed to have smuggled the bomb through a back entrance at the airport and placed the bomb on the back of the plane. They also claimed to have a friend in airport security help them get through.

The person ended the series of tweets by threatening more flights if anything were to happen to him or her.