Suella Braverman has come under widespread criticism in recent weeks over her management of the Home Office.
Braverman has been condemned for her handling of the migrant crisis - but Abbott also faced a backlash following her comments.
Almost 40,000 people have crossed the Channel on small boats and dinghies so far this year.
The Tory MP for the Isle of Wight said he was 'really unhappy with the situation' in his party.
The home secretary has received backlash after saying she wanted to cut welfare spending due to a “benefits street culture”.