The proposed purchase of Seven & i Holdings would be the biggest ever foreign takeover of a Japanese firm and combine 7-Eleven, Circle K and other brands across Asia, North America and Europe.
As the world's biggest convenience store chain, 7-Eleven operates more than 85,000 outlets globally.
Although the brand began in the United States, since 2005 it has been wholly owned by Seven & i.
A letter from the Seven & i board to Alimentation Couche-Tard (ACT) said it was open to "engaging in sincere discussions should you put forth a proposal that fully recognises our standalone intrinsic value".
"We do not believe, for several critical reasons, that the proposal you have put forward provides a basis for us to engage in substantive discussions regarding a potential transaction," it said.
ACT operates more than 16,700 outlets in 31 countries and territories.
Its purchase of Seven & i would be the biggest ever foreign takeover of a Japanese firm and create an international convenience store behemoth combining 7-Eleven, Circle K and other brands across Asia, North America and Europe.
Seven & i said ACT had offered $14.86 per share in cash, which roughly matches its market value of $39 billion.
But the board's letter called the proposal "opportunistically timed" and said it "grossly undervalues our standalone path and the additional actionable avenues we see to realise and unlock shareholder value".
It also raised regulatory concerns.
"Your proposal does not adequately acknowledge the multiple and significant challenges such a transaction would face from US competition law enforcement agencies," it said.
A quarter of 7-Eleven stores are found in Japan where they are a beloved institution, selling everything from concert tickets to pet food and fresh rice balls.
Seven & i Holdings' other businesses include a major supermarket operator, restaurant chain Denny's, and Tower Records -- a once-popular US record store that went bankrupt.
Seven & i has reportedly asked the Japanese government to designate parts of the company as "core", which would make a takeover more difficult.
Brands with the "core" rating in Japan include manufacturers in the nuclear, space, rare earths and chip industries, as well as cybersecurity and infrastructure operators.
The Canadian firm, however, is confident that it can have its way.
CEO Brian Hannasch told an earnings briefing in New York on Thursday that Couche-Tard could "even consider a higher leverage if needed", indicating it has the capacity to raise more funds, according to Nikkei Asia.
"We have the solid and robust balance sheet," Nikkei quoted Hannasch as saying.
Shares in Seven & i were down 1.9 percent in Tokyo on Friday.
