The agency says it is offering registration to those who want to travel to the US from Canada and Mexico, or to Europe from the US.
It says it has been able to identify around 5,000 travellers from countries around the world who have applied.
The agency has also been able tell which of the 5,937 passengers were using a passport or visa that expired before January 1, 2018.
The airline says it can’t be held responsible for the expired visa or passport if someone has been in the US for more than three months.
Icef says it will accept all new US and Canadian travellers who apply for an expired visa, passport, or Canadian tourist visa.
The company says it could accept up to a year of validity for US travellers, with those in Canada who want a longer visa extension to apply for.