(Adds reports of AustralianSuper lifting stake in paragraph 5; comment from Brookfield executive in paragraphs 8 and 9)

By Lewis Jackson and Scott Murdoch

SYDNEY, Nov 13 (Reuters) - Australian pension fund AustralianSuper said on Monday it had rejected an "eleventh hour" offer from a Brookfield-led consortium and its partner EIG to drop its opposition to their $10.5 billion bid for Origin Energy and join the takeover.

Australia's largest pension fund reaffirmed its intention to reject the bid at the shareholder meeting on Nov. 23, hours after receiving the consortium's "unsolicited" offer, the fund said in a statement.

"AustralianSuper’s position is unchanged on the upcoming vote ... as we believe the offer remains substantially below our estimate of Origin’s long-term value," a spokesperson said.

AustralianSuper said it was Origin Energy's largest shareholder, but did not specify the size of its stake as it has done in previous releases.

The Australian Financial Review reported late on Monday the fund had raised its stake to 16.5% from 15%. AustralianSuper declined to comment.

The moves come just under two week since the A$300 billion fund turned down an improved "best and final" A$9.53 per share bid from the group and threatens to scupper the buyout of Australia's largest energy retailer.

While AustralianSuper's stake is below the quarter threshold required to block a bid, generally low turnout from the retail shareholders who make up about a third of the listing gives the fund's stake extra weight.

Brookfield argues its bid, which comes with the commitment of A$20 to A$30 billion worth of investment, will decarbonise Origin Energy faster than if the company remains in public hands.

"We’re offering a clear pathway to a faster reduction of the company’s emissions and an acceleration of Australia’s net zero targets," Brookfield Managing Director of Renewable Power & Transition Luke Edwards said in a statement.

However, AustralianSuper said on Monday it was also open to stumping up cash to fund Origin's transition. (Reporting by Lewis Jackson in Sydney; Editing by Alasdair Pal, Stephen Coates & Shri Navaratnam)