Former prime minister Tony Abbott has given further hints he may be considering staying on in the Federal Parliament and suggested the public will better appreciate his legacy with the passage of time.

Mr Abbott, who was ousted as prime minister in a leadership coup last month, also confirmed his relationship with Bronwyn Bishop had deteriorated, as a result of her being dumped as speaker over her grandiose use of entitlements.

The former prime minister returned to life as a local member in his northern Sydney electorate of Warringah this week, visiting a local school that had recently lost five classrooms in a fire.

"I was really impressed with the way that students and teachers at Seaforth Public School have come together after a fire recently burnt down five classrooms," Mr Abbott wrote on Facebook.