* PPG's bid is 50 pct premium to Akzo's shares before first offer
* Akzo says it will consider bid according to its legal duty
* Company's boards will face questions from shareholders Tuesday (Updates with details, quotes.)
By Toby Sterling
AMSTERDAM, April 24 (Reuters) - PPG Industries, the U.S. paintmaker that is pursuing a takeover of Dutch peer Akzo Nobel, on Monday increased its proposed cash and share offer to 26.9 billion euros ($28.8 billion, from around 24.6 billion euros.
The move comes a day before Akzo, which has declined two previous approaches from PPG, faces a group of unhappy shareholders at its annual meeting. Akzo shares jumped 6 percent to a record high of 82.86 euros by 1130 GMT.
The shareholders, led by hedge fund Elliott Advisors, say Akzo should at least open exploratory talks with PPG to more closely examine their proposal.
"We are extending this one last invitation to you and the AkzoNobel boards to reconsider your stance and to engage with us," PPG Chief Executive Michael McGarry said in a statement on Monday.
"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," added McGarry.
Akzo Nobel confirmed it had received a "third unsolicited proposal" from PPG but was non-committal in its response.
"The Board of Management and Supervisory Board of AkzoNobel will carefully review and consider this proposal," said Akzo, whose brands include Dulux paint.
A spokesman for Elliott said the fund was examining PPG's latest proposal and could not immediately comment.
PPG said its bid represented an increased price of 96.75 euros, including dividend, per AkzoNobel share -- comprised of 61.50 euros in cash and 0.357 shares of PPG common stock.
That is a 50 percent premium from Akzo Nobel's closing price of 64.42 on March 8, the day before PPG confirmed it had made a proposal to buy Akzo at 80 euros per share.
A second bid worth 90 euros per share on March 20 was rejected within 48 hours, with Akzo arguing that it substantially undervalued the company and would be bad for other stakeholders, such as employees and customers.
Last week, Akzo presented its case for remaining independent, offering shareholders 1.6 billion euros in extra dividends and detailing plans to sell or float its chemicals arm, representing a third of company sales and profits, within one year.
Both moves, if completed, would make Akzo a less attractive target for PPG, although the Pittsburgh-based company has said the primary reason for the merger would be synergies of $750 million between the companies' paints and coatings businesses. (Reporting by Toby Sterling. Additional reporting by Maya Keidan. Editing by Keith Weir/Jason Neely)