The warning early on Sunday morning (local time) says US citizens should avoid travelling to the airport and avoid all airport gates at this time.
It specifically noted the South (Airport Circle) gate, the new Ministry of the Interior, and the gate near the Panjshir Petrol station on the northwest side of the airport.
A suicide bombing at the airport on Thursday killed at least 169 Afghans and 13 US service members.
It comes as US President Joe Biden vowed to keep up airstrikes against the Islamic extremist group responsible for the attack.
He warned another attack was "highly likely" and the State Department called the threat "specific" and "credible."
The Pentagon said the remaining contingent of US forces at the airport, now numbering fewer than 4000, had begun their final withdrawal ahead of Mr Biden's deadline for ending the evacuation on Tuesday.
After getting briefed on a US drone mission in eastern Afghanistan that the Pentagon said killed two members of the Islamic State group's Afghanistan affiliate early Saturday, Mr Biden said the extremists can expect more.
"This strike was not the last," Mr Biden said in a statement. "We will continue to hunt down any person involved in that heinous attack and make them pay." He paid tribute to the "bravery and selflessness" of the American troops executing the hurried airlift of tens of thousands from Kabul airport, including the 13 US service members who were killed in Thursday's suicide bombing at an airport gate.
The evacuation proceeded as tensions rose over the prospect of another IS attack. The State Department issued a new security alert early on Sunday morning Kabul time instructing people to leave the airport area immediately "due to a specific, credible threat."
"Our commanders informed me that an attack is highly likely in the next 24-36 hours," Mr Biden said, adding that he has instructed them to take all possible measures to protect their troops, who are securing the airport and helping bring onto the airfield Americans and others desperate to escape Taliban rule.
The remains of the 13 American troops were on their way to the United States, the Pentagon said. Their voyage marked a painful moment in a nearly 20-year American war that cost more than 2,400 US military lives and is ending with the return to power of a Taliban movement that was ousted when US forces invaded in October 2001.
The Pentagon released the names of those killed — 11 Marines, one Navy sailor and one Army soldier. Twelve of them were in the 20s; some were born in 2001, the year America's longest war began. The oldest was 31.
They were the first US service members killed in Afghanistan since February 2020, the month the Trump administration struck an agreement with the Taliban in which the militant group halted attacks on Americans in exchange for a US agreement to remove all troops and contractors by May 2021. Mr Biden announced in April that the 2500 to 3000 troops who remained would be out by September, ending what he has called America's forever war.