The offer, of 96.75 euros per AkzoNobel share, is 8% more than it offered on 22 March, and 17% more than its opening offer made on 2 March.
AkzoNobel has been trying to repel the bid by announcing plans to spin off its chemicals unit and return most of the proceeds to shareholders.
PPG said the new offer was AkzoNobel's last chance to accept the deal.
"We are extending this one last invitation to you and the  AkzoNobel boards to reconsider your stance and to engage with us on creating extraordinary value and benefits for all of AkzoNobel's stakeholders," said PPG's chairman and chief executive, Michael McGarry.
"Our revised proposal represents a second increase in price along with significant and highly-specific commitments that we are confident  AkzoNobel's stakeholders will find compelling," he added.
The revised offer, in a mixture of cash and PPG shares, would value AkzoNobel at 24.6bn euros which, PPG said, was a 50% premium over the the Dutch group's value as of 8 March.
The latest offer is critical of AkzoNobel's own plan, announced on 19 April, to split the Netherlands-based group into two: one part concentrating on paint and the other on chemicals.
PPG said: "As evidenced by the decline in AkzoNobel's stock price since its investor update, the capital markets have not recognized any additional value from its new standalone plan, including the enhanced regular dividend and special dividend that AkzoNobel has proposed for 2017."
"One of the more notable risks of AkzoNobel's new standalone plan is that it creates two smaller, unproven standalone companies with uncertain market valuations and substantial risks.
"AkzoNobel's standalone plan also will require substantial restructuring; potentially decreases free cash flow, putting future and accelerated growth plans of the demerged companies at risk," added PPG.
PPG said that by contrast a merger of the two firms would lead to savings of at least $750m a year for the combined firm.
To make the suggested deal more acceptable to shareholders and other stakeholders in the Netherlands, the latest PPG offer outlines a long list of commitments to retain AkzoNobel's links with that country:
US paint firm PPG has increased its proposed  bid for Dulux owner AkzoNobel for the second time.