Suella Braverman is under pressure to answer questions about worsening conditions at a migrant processing centre in Kent said to be overcrowded.
The home secretary faces demands from Labour and a senior Tory MP to address the Commons over the situation at the site in Manston.
Hundreds of people were moved there on Sunday after a fire attack at a separate migrant facility in Dover.
The government said it was controlling immigration and deterring traffickers.
Immigration Minister Robert Jenrick and Tory MP Sir Roger Gale visited the Manston centre on Sunday to discuss solutions to ease pressure on the site.