U.S. private equity firm Blackstone Group plans to lift its bid for Australian real investment trust Investa Office Fund to A$3.3 billion ($2.4 billion) to beat a rival offer from Canadian real estate developer Oxford Properties Group.

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 $8.6 million above Oxford’s price if Investa agreed, among other conditions, to recommend it and lift the deal’s break fee.

Investa shares touched a nearly 10-year peak rising 1.4 percent to Blackstone’s offer price of $3.96 per share. Oxford, which already owns 10 percent of Investa, offered $3.95 per share, and Blackstone’s previous bid was for $3.84 per share.