About 4,000 people have either been deported or moved to other processing centres, according to DHS.
From Thursday, flights could be ramped up to as many as seven a day, according to the Washington Post.
Quoting an unnamed US official, the Associated Press also reported on Tuesday that authorities are also releasing Haitian migrants into the US “on a very, very large scale”.
The official added that many of the migrants have been given notices to appear at immigration offices within 60 days. The official said this approach requires less processing time than having them appear before an immigration court.
The migrants have been waiting in a makeshift camp in temperatures of 37C (99F).
Local officials have struggled to provide them with food and adequate sanitation.
Most of those at the camp are Haitians, but there are also Cubans, Peruvians, Venezuelans and Nicaraguans present.
Meanwhile the Colombian government has said that around 19,000 migrants – mainly from Haiti – are stranded near the border with Panama. Migrants often cross into Panama and proceed on foot as part of a long journey north towards the United States.
However, a senior Colombian official said that many migrants are now stranded near the border as a result of an agreement between the two countries restricting the number of migrants crossing the Gulf of Urabá into Panama to just 250 people a day.
He added that many migrants have been risking their lives by trying to cross the gulf illegally at night on substandard boats.
Many Haitians left the country after a devastating earthquake in 2010, and a large number of those in the camp had been living in Brazil or other South American countries and travelled north after being unable to secure jobs or legal status.
This year has brought further hardship for the impoverished country. In July, Haiti’s president was assassinated – and in August it suffered another deadly earthquake.
