The bidding war heats up the tussle for the owner of 20 office towers as commercial rents boom, especially in Sydney where Investa's holdings are concentrated and downtown capacity is tight.

Blackstone, seemingly set to seal its takeover until Oxford's last-minute bid on Tuesday, wrote to Investa offering A$12 million above Oxford's price if Investa agreed, among other conditions, to recommend it and lift the deal's break fee.

Investa, which published Blackstone's late-night letter and adjourned a shareholder vote on the buyout on Thursday while it mulls Oxford's offer, said in a statement it intends to work with Blackstone to meet the conditions. It recommended the deal.

An Oxford spokeswoman in Sydney had no immediate comment.

"The whole sector is on a tear," Morningstar property analyst Tony Sherlock told Reuters.

"It's that powerful search for yield from overseas that's spilling over into Australia ... the fact that the share price keeps jumping each time it happens, the market's not expecting this," he added.

Investa shares touched a nearly 10-year peak on the news, rising 1.4 percent to Blackstone's offer price of A$5.52, suggesting the market is confident at least one of the deals will proceed.

Oxford, which already owns 10 percent of Investa, offered A$5.50 per share, and Blackstone's previous bid was for A$5.3485 per share.

The prospect of a sweetener comes a day after Blackstone threatened to walk away from its offer if Investa adjourned Thursday's meeting and deemed Oxford's offer superior.

Blackstone now wants Investa to reschedule the meeting as quickly as possible and before Sept. 14.

"The acquirers consider this in increase in price to be extremely attractive," Blackstone's Head of Real Estate Australia, Chris Tynan, wrote in the letter to Investa.

Australia's commercial property sector has defied a softening in home values. With overall unemployment sitting at a six-year low, economic growth surging and city downtown capacity barely growing, demand is outstripping supply.

British-based consultant Oxford Economics forecasts vacancy rates for Sydney offices to hit an all-time low of 3 percent by the end of 2019.

Betting that would lift rents, Investa shareholders rejected a A$2.5 billion takeover from rival Dexus at A$4.11 per share two years ago.

(Reporting by Tom Westbrook in SYDNEY. Additional reporting by Aaron Saldanha in BENGALURU; Editing by Stephen Coates)

By Tom Westbrook