A security alert on Saturday told US citizens to stay away due to possible “security threats outside the gates”.
Only those individually told to make the journey by a US government representative should do so, it said.
US defence officials said they were monitoring developments and looking at alternative routes.
No further details were given about the potential threat of an IS attack, and the group has not publicly threatened to carry out attacks in Kabul.
The US advice on Saturday came amid continued chaos outside the airport terminal and reports of people being crushed as thousands attempt to escape from Afghanistan following the Taliban takeover.
Crowds have been gathering daily, hoping to be allowed on to a flight. Those who work with the US and its allies, as well as people who have campaigned on issues like human rights, fear they may face reprisals at the hands of the Taliban if they are unable to leave.
What exactly has been happening at the airport gates on Saturday remains unclear.
However, Sky News’ chief correspondent Stuart Ramsay said that people at the front of the crowd of thousands were being “crushed to death”, with British soldiers pulling those in danger from the throng.
He has described it as “the worst day by far”, and said they believed people had died at the scene.
In a briefing on Saturday, the US Department of Defense said 17,000 people had been flown out of the airport, including some 2,500 US citizens.
An official said a “small number” of Americans and Afghans the US wanted to evacuate had faced harassment. In some cases, they had been beaten on their way to the airport.
A spokesperson for the US State Department later told the BBC they issued the guidance to avoid large crowds outside the airport gates.
It is also because they now have the capacity to communicate with US citizens “on a personalised basis”, to give them “tailored instructions” on how to travel, the spokesperson said.
Other countries have also warned about the situation on the ground.
Germany’s government issued a statement saying the airport remains “extremely dangerous and access to the airport is often not possible”, while the Swiss foreign ministry announced the security situation had “deteriorated significantly in the last few hours” and postponed a chartered evacuation flight from Kabul.
US forces are currently controlling the international airport. They are helping to evacuate their own citizens and those of other countries, including Afghans who worked with Western forces and fear for their safety under the Taliban.
But the US has set a withdrawal date of 31 August for their troops, and it is unclear what will happen after this date. (Courtesy BBC)