Tony Abbott has refused to buy into explosive new claims that his colleagues believed he was having an affair with his chief-of-staff, Peta Credlin.

A new book by News Corp columnist and former Coalition staffer Niki Savva contains fresh claims that a number of government frontbenchers warned him that his job was under threat unless he sacked the divisive Ms Credlin.

Confronted about the claims at Sydney Airport on Saturday, Mr Abbott said he did not want to "rake over old coals".