The latest bus with 44 migrants on board arrived at Union Station on Saturday from Brownsville, Texas.
They were from Mexico, Colombia, China, Haiti, Honduras, Peru and Venezuela. Fourteen of them were children between 2 to 14 years old.
They were taken to Cathedral High School in Chinatown where they were evaluated for medical issues and given food.
Officials say about 150 to 160 people have arrived in the past five weeks. Officials say as more people arrive resources are getting scarce.
Jorge Mario Cabrera with the Coalition for Humane Immigrant Rights (CHIRLA) says when migrants arrive, they "will be received with dignity and respect."
"However, we have to make clear that our resources are not unlimited," Cabrera said.
This is the fifth bus to arrive in L.A. since June 14. According to some estimates, Abbott has bused or sent 20,000 migrants to democratically-run cities and states.
"You look what's going on in New York. They have more than 50,000 migrants staying in shelters every single night there," said Ira Mehlman with the Federation for American Immigration Reform.
Mehlman said the fact that Los Angeles and New York are complaining about a lack of resources is what Abbott has been saying for years. Mehlman is also concerned about how these limited services will affect others.
"When you have more people trying to access these services, then there are resources available to provide them," Mehlman said. "It is going to affect everyone, and is going to affect the people who have a legitimate cause to be in Los Angeles and to be in the United States. They are going to be the ones who are losing out."
A big concern is the number of people on the streets in Los Angeles. Officials claim so far they've been able to get people housed with families or others.
"Obviously, it includes individuals who may not have a place to go amongst these asylum seekers. So far most of them have found a place either with loved ones, family members or sponsors," Cabrera said.
The one thing both sides agree is that the immigration system needs to be fixed.
"The immigration system in the United States is indeed broken," Cabrera said. "However, our hearts cannot be broken."
Mehlman adds: "What they need to do is to be working across party lines, across state lines to send a very clear signal to the administration - this has got to stop."
Officials in L.A. say they need help to deal with the increasing number of arrivals, but they stress despite limited resources they will continue to do as much as they can.