The Dutch firm said the 26.9bn euro (Â£22.8bn) offer undervalued Akzo and showed a "lack of cultural understanding of the brand".
The company, which claims its own plans for growth are superior, has been urged to reject a merger by the Dutch government and its own workers.
But some Akzo investors favour a deal.
PPG said it was disappointed by Akzo Nobel's decision and would "review" the firm's response.
It comes several weeks after PPG increased its offer to buy the Amsterdam-based firm for the second time as it seeks to create an industry leader in the paints and coatings sector.
The US firm suggested the bid was its last friendly attempt to merge with Akzo and has not ruled out putting the matter directly to shareholders.
But responding on Monday, Akzo chief executive Ton Buchner said his team had conducted an "extensive review" of the bid and had again found it wanting.
"The PPG proposal undervalues AkzoNobel, contains significant risks and uncertainties, makes no substantive commitments to stakeholders and demonstrates a lack of cultural understanding," he said.
Akzo says its own plans for the firm - which involve spinning off its chemicals division into a separate business - would better serve shareholders.
It has promised to increase its dividend for 2017 by half and pay a 1bn euro special cash dividend in November.
However, it also faces mounting pressure from some of its biggest shareholders to consider a deal, having repeatedly refused to enter talks with PPG's management.
Last month, the activist investor Elliot Investors also called for a vote to oust chairman Antony Burgmans - a proposal Akzo rejected.
In its favour, Akzo has won political support against a tie-up, with four provincial governments having warned of its impact on jobs.
The company also says that PPG would struggle to get the deal past Dutch competition regulators, which poses a risk to shareholders.
As part of its latest offer, PPG offered commitments on jobs and to pay a break fee in case the deal was rejected by officials.
In a statement on Monday, it said: "[Akzo] has once again refused to enter into a negotiation regarding a combination of the two companies, ignoring the best interests of its stakeholders, including long-term shareholders who overwhelmingly support engagement."
Akzo Nobel shares fell more than 2% in morning trading in Amsterdam but have jumped about 30% this year.

The 22-year-old was an unused squad member during the 2017 Six Nations, as well as the 2016 autumn internationals.
"It's been building as I've been in a few camps now, but to finally get my name called out on that team sheet was an awesome feeling," he said.
"I've been champing at the bit these last few camps, training hard."
The Ospreys player comes in to replace Cory Hill, who was called up by the British and Irish Lions following Wales' 24-6 win over Tonga.
Coach Robin McBryde has made seven changes in all to the side that started that game at Eden Park last Friday
Another two uncapped players - scrum-half Tomos Williams and lock Adam Beard - are also on the bench.
Media playback is not supported on this device
Thornton made 25 appearances for Ospreys in the 2016-17 campaign, but expects a big transition to international rugby.
"I've been playing a lot for the Ospreys this year and being involved in the Pro12 and the [European] Challenge Cup has given me quite a bit of experience," the former Wales Under-20s captain told BBC Wales Sport.
"But Test rugby is a completely different animal, so I'm really looking forward to the challenge on Friday against a strong Samoan team.
"Like every young Welsh boy I want to play for Wales, but when it actually comes round you get that sensation of pride."
Thornton is part of an inexperienced Wales side, with the forwards having won just 31 caps between them.
"Samoa have a big experienced pack and we have a couple of young guys here looking to blood themselves on the international stage, so I think it'll be a good challenge overall," Thornton added.
Media playback is not supported on this device
Akzo Nobel, the owner of Dulux paint, has rejected a third takeover offer by US rival PPG Industries, leaving the door open to a hostile bid.
[NEXT_CONCEPT]
Lock Rory Thornton says he is "champing at the bit" ahead of winning his first Wales cap against Samoa in Apia on Friday, 23 June.