That's up from its earlier offer valued at $2.6 billion.
Baytex raised its offer to roughly $4.29 per Aurora share or $4.20 in Australian dollars, up from roughly $4.18 or $4.10 in Australian dollars.
The sweetened offer has the support of two of Aurora's large shareholders, Harbour Advisors and Stirling Global Value Fund Inc., which hold together roughly 17.4 per cent of Aurora's shares.
Aurora shares (TSX:AEF) were up 25 cents at $4.26 in trading on the Toronto Stock Exchange.
Aurora shareholders will vote on the offer on May 21 in Perth, Australia.
The acquisition will allow Calgary-based Baytex to expand into the lucrative Eagle Ford shale in Texas.
Once the deal closes, Baytex's core operating areas will include the Eagle Ford, Peace River oilsands in northwestern Alberta and Lloydminster heavy oil near the Alberta-Saskatchewan border. At that point, its total production is expected to be 85,000 barrels of oil per day.
With the Aurora assets, Baytex will be 53 per cent heavy oil, 34 per cent light oil and 13 per cent natural gas. The current breakdown is 75 per cent heavy oil, 14 per cent light oil and 11 per cent natural gas.
Most of the Eagle Ford acreage included in the deal is operated by a subsidiary of Marathon Oil Corp.
Aurora, whose head office is in Australia, trades on the Australian and Toronto stock exchanges.