Murray Goulburn Co-operative hiked its all-cash bid to $9.50 Australian dollars, about 5.6 per cent above its own previous bid of AU$9.
The C$514.8 million (AU$532.9 million) bid is nearly AU$17 million more than Saputo's highest offer.
The Montreal-based cheese giant on Monday offered up to AU$9.20 per Warrnambool share if it gets majority ownership, or AU$9 if it doesn't get more than half of the Australian company's stock.
Murray Goulburn said the takeover will have "significant ramifications" for the future of the Australian dairy industry as a whole and urged shareholders to take a "long-term view."
"The revised offer is a further endorsement of Murray Goulburn's commitment to acquiring WCB, and delivers an Australian owned and operated company with the scale, capacity, strength and momentum to capture global growth opportunities," it stated in a news release.
The co-operative also said it wants Warrnambool to consider reinstating special dividends so some shareholders can obtain "franking" or tax credits under its revised offer. Saputo (TSX:SAP) removed this feature from its last offer.
Murray Goulburn's offer is AU$2.01 above the top end of an independent expert's assessed value range for WCB shares. It also represents a 111 per cent premium over the AU$4.51 closing price for WCB shares on the last day before an offer by Bega Cheese launched the three-way cheese war.
The board of Warrnambool Cheese and Butter has advised its shareholders to take no action at this time in response to Murray Goulburn's revised bid.
Warrnambool said its Australian suitor has continued to attach conditions on its takeover offer, including getting approval for the deal from competition authorities that could take three to six months.
Irene Nattel of RBC Capital Markets said the bidding hasn't likely ended since neither Murray Goulburn nor Saputo has described their bid as firm and final.
"Magnitude of incremental increases clearly moderating, suggesting that we are getting closer to the top on price," she wrote in a report.
On the Australian Stock Exchange, Warrnambool's shares closed at AU$9.32 on Thursday after peaking at AU$9.45 in intraday trading. They are increased from AU$3.50 set last March. Saputo's shares gained six cents at C$48.34 in morning trading on the Toronto Stock Exchange.
Nattel said Saputo views the Warrnambool acquisition as strategic because it will deliver little or no incremental earnings as the bidding price increases.
"Saputo will have to decide how much it is willing to pay to realize its strategic objective of a foothold in Oceania," she added.
Saputo has been eyeing expansion into the region for years to develop its reach into the Asia Pacific area and capitalize on growing global demand for dairy solids.
Australia is the world's third-largest exporter of milk products after the European Union and New Zealand, with about 10 per cent global market share.
Murray Goulburn's higher bid comes after it asked the Australian Takeovers Panel to intervene in Saputo's bid, claiming its Canadian cheese rival misinformed shareholders about the true value of its latest offer.