Washington (CNN) Three Central American parents are suing US immigration officials for more communication with their children who were separated from them after they crossed the US-Mexico border illegally.

In a court filing Thursday, lawyers for the three parents alleged that immigration authorities are not ensuring ample communication between the parents and their young children.

The children mentioned in the lawsuit are among the less than 3,000 children estimated to have been separated from their parents. Health and Human Services Secretary Alex Azar released the new estimate on Thursday during a call with reporters nearly two weeks after HHS provided an exact figure of 2,053 children in their care.

The Texas Rio Grande Legal Aid lawyers detailed some of the "various hurdles in arranging communications" for the parents and their children in the joint status report, filed as part of an ongoing lawsuit brought in DC federal court against top Department of Homeland Security and Health and Human Services officials.

One plaintiff, a Honduran citizen, only spoke to his 12-year-old daughter on Tuesday -- a month after the pair was separated, the legal aid lawyers claim.

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