Transat in June accepted Air Canada's all-cash bid of C$520 million ($394 million), or C$13 a share, over a C$14 per share offer from Mach.
Mach said it plans to use the purchased shares to vote against the Air Canada-Transat deal, saying the offer "greatly undervalues" Transat.
The latest offer represents a 21.2% premium to Transat's Thursday close of C$11.55.
Mach also said it has no intention to launch a formal hostile takeover bid and added that it will not raise the C$14 offer as long as the current Transat board is in place.
Mach said last month that its buyout proposal had become null and void after Transat accepted Air Canada's bid and that it had not withdrawn the offer.
The offer had raised questions after Mach initially said it needed government financing to complete the deal, a condition it waived in June.
Transat is required to pay C$15 million if it backs out of the agreement in favor of a fully financed offer of C$14 a share or more that is not matched by Air Canada.
Air Canada would need approval from two-thirds of Transat shareholders for the deal to go through.
Transat said a special committee of its board was reviewing Mach's latest offer and advised shareholders to not tender shares until a formal recommendation.
Scotiabank analysts said Transat shareholders, employees, and the Canadian government would find "the most value creation for all" in an Air Canada-Transat deal, unless rival airlines showed an interest.
"Our initial view is that Mach's second attempt to derail the AC/TRZ merger lacks merit, because we don't see a clear strategic rationale in its disclosed proposal against what we expect to be a meaningfully synergistic AC/TRZ merger," the analysts said.
(Reporting by Arathy S Nair in Bengaluru and Allison Lampert in Montreal; Editing by Shinjini Ganguli and Sriraj Kalluvila)