Abella made this announcement in a statement issued on Wednesday, a day after Interior and Local Government Secretary Ismael D. Sueno was sacked.
Duterte said he has also "fired" a longtime ally from Davao City due to allegations of corruption.
Sueno supported Duterte's presidential bid a year ago and had previously served as a mayor and a governor.
Undersecretary Catalino S. Cuy will occupy Mr. Sueño's position in a holdover capacity, "effective immediately", Mr. Abella said.
"It appears that from the very start, they want my head and are out to discredit me because they want somebody else to head the department", he said this week during a flag-raising ceremony at the Interior Ministry.
Abella said the announcement was made at the end of the 14th Cabinet Meeting that was held in Malacanang on Monday night.
Duterte spoke before a gathering at the Metro Manila Development Authority in Makati City, a day after firing Department of Interior and Local Government Secretary Mike Sueno.
Muslim man killed by mob of 'cow vigilantes'
One officer, Ramesh Chand Sinsinwar, told the AFP news agency the men were transporting the animals without permission. The assailants were believed to be members of right-wing groups Hindu Jagaran Manch and Bajrang Dal.
DILG undersecretaries John Castriciones, Jesus Hinlo, and Emilie Padilla have reportedly called on Duterte to remove Sueno, whom they accused of collecting grease money from illegal gambling rings through his grandson, a police official identified only as "Senior Superintendent Sintin".
"Yes, for some guidelines and to inform them that Usec". There were reports however that another ranking official is set to be axed by Duterte.
The Chief Executive cited loss of trust and confidence following allegations of corruption and abuses heaped against Sueno.
"I do not have to belabor the point", Duterte said afterward.
The first to leave government was the President's former campaign spokesman, Peter Laviña, who headed the National Irrigation Administration.
Duterte on Sunday announced that he will be dismissing an official in government over alleged corruption charges but declined to give details.
1-Ang Edukasyon party-list Rep. Salvador Belaro Jr. agreed that Sueno should be investigated and charged if there is any evidence to pin him down on allegations of corruption.