The Foreign Ministry yesterday said the six have not technically entered Colombian territory.
Despite ideological differences, Colombia and Cuba maintain relatively good relations and the communist-led island nation has been hosting peace talks in Havana over the past year between the Bogota government and Colombia's main leftist rebel group.
All six Cubans arrived on flights from Ecuador's capital, Quito, after being rejected by that country.
Ecuador does not require visas but since January 2013 has demanded that Cuban visitors obtain formal letters of invitation in advance of their arrival. The requirement was established because so many Cubans were illegally taking up residence in Ecuador.
The Cubans remaining at Bogota's airport told an Associated Press reporter that they did not want to return to their homeland because they feared persecution.
One of them, Angel Barrios, said he had an Ecuadorean invitation letter but it was rejected and torn up in Quito. An adviser to Ecuador's Interior Ministry reached in Quito, Camilo Marquez, said he did not have details of the case.