This latest offer is Independent's fourth since October and cannot be raised again once it is declared final under Australian takeover laws.
Independent already owns around 42% of APN. The Australian company publishes more than 120 newspapers in Australia and New Zealand, including the New Zealand Herald, and owns several radio stations.
Shares in APN News were trading at A$6.04 (£2.52) today.
IN&M, which publishes 175 newspaper and magazine titles across the globe, plans to reduce its stake in APN to 35% from 42%, while Carlyle will hold 27.5% and Providence 37.5%.
Australian media laws were altered on April 4, relaxing foreign ownership limits and allowing cross-ownership of different forms of media in the same market. Analysts predict this will trigger a wave of consolidation in the industry.