
Foreign Minister Julie Bishop and Communications Minister Malcolm Turnbull had told Abbott to resign, Sky reported, citing unidentified sources.
Turnbull, seen as Abbott's most likely challenger, has called a media conference at Parliament House later on Monday.
Abbott emerged badly weakened from a leadership challenge by lawmakers in his own Liberal Party in February, which came about after weeks of infighting and dismal poll numbers, and pledged a new spirit of conciliation.
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