Australia, the US and UK have issued alerts to their citizens. Those already outside the airport are advised to leave the area immediately.
More than 82,000 have been airlifted from Kabul, which fell to the Taliban 10 days ago.
Countries are rushing to evacuate people by a 31 August deadline.
Thousands of people are still waiting inside and outside the airport, hoping to fly out of the country.
The Taliban have opposed extending the deadline but also promised to allow foreigners and Afghans to leave the country beyond 31 August, according to US Secretary of State Antony Blinken.
On Thursday, Australia’s Minister for Foreign Affairs, Marise Payne, said: “There is an ongoing and very high threat of a terrorist attack”.
It comes hours after the US State Department told those waiting at the Abbey Gate, East Gate or North Gate to “leave immediately”.
The UK issued similar advice asking people there to “move away to a safe location and await further advice“.
The Foreign Office said that the security situation in Afghanistan “remains volatile” adding that there was “an ongoing and high threat of a terrorist attack”.
None of the countries gave any further information on the security threat. (Courtesy BBC)