The new proposal offered to buy all shares at some 96.75 euros per share, an increase of 6.75 euros on its last bid on March 21.
In its third offer since March, PPG's chairman and chief executive Michael McGarry said he was making "one last invitation" to AkzoNobel to "engage with us on creating extraordinary value and benefits for all of AkzoNobel's stakeholders."
The new proposal offered to buy all shares at some 96.75 euros per share, an increase of 6.75 euros on its last bid on March 21. That would increase the value of the company from some 22.4 billion euros to 24.6 billion euros ($26.6 billion).
"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," McGarry wrote in a letter to the company bosses.
AkzoNobel's paint-making business, which includes such brand names as Dulux and Trimetal, is seen as a broad barometer of underlying global economic activity.
It said in a statement Monday that it "will carefully review and consider this proposal" which it said was "a third unsolicited and conditional proposal" from PPG.
The company has come under pressure in recent weeks after already twice rejecting offers in the increasingly hostile takeover battle with the Pittsburg-based PPG.
Last week, the Amsterdam-based company unveiled plans to spin off its specialist chemicals division either via a sale or a separate listing within the next 12 months, hoping to calm rumblings among shareholders discontent with the rejection of PPG.
Buoyed by stronger-than-expected first-quarter profits, AkzoNobel chief executive Ton Buchner valued the chemicals division at between eight and 12 billion euros.
"We will create two focused and high-performance businesses," he said.
"Both businesses have skills and capabilities to stand on their own and to deliver a strong cash generation in the future."
But PPG said Monday it believed its new offer was "vastly superior to AkzoNobel's new standalone plan."
McGarry argued that "one of more notable risks" of AkzoNobel's new plan "is that it creates two smaller, unproven standalone companies with uncertain market valuations."
It would also require "substantial restructuring" for the company.
The "revised proposal offers a value to AkzoNobel's shareholders that is well in excess of AkzoNobel's ability or track record to create value on a standalone basis," he argued.